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⊙ 주요 논문 :

 

  1. ● Harmonic spaces and density functions (joint with P. Gilkey), Results Math. 75 (2020), no. 3, Paper No. 121, 18 pp.

    ● Quasi contact metric manifolds with Killing characteristic vector fields (joint with J. Bae, Y. Jang, and K. Sekigawa), Bull. Korean Math. Soc. 57 (2020), no. 5, 1299–1306.

    ● Einstein hypersurfaces of the Cayley projective plane (joint with S Kim, Y Nikolayevsky), Differ. Geom. Appl. 69 (2020), 101594, 6 pp.

    ● Totally geodesic submanifolds of Damek-Ricci spaces (joint with S Kim, Y Nikolayevsky), to appear Revista Mathematica Iberoamericana.

    ● Affine Killing complete and geodesically complete homogeneous affine surfaces (joint with P. B. Gilkey, J. H. Park, and X. Valle-Regueiro), Journal of Mathematical Analysis and Applications. J. Math. Anal. Appl. (2019), 474, (1) 179-193.

    ● Notes on minimal unit Killing vector fields (joint with S. Chun, and K. Sekigawa), Bull. Korean Math. Soc. 55 (5) (2018), 1339-1350.

    ● A one-parameter family of totally umbilical hyperspheres in the nearly Kaehler 6-sphere (joint with J. Baeand K. Sekigawa), J. Korean Math Soc. 55 (2018) 4, 963-974.

    ● Characterizing the harmonic manifolds by the eigenfunctions of the Laplacian,

    (joint with J. Choe and S. Kim)J. Geom. Phys. 126 (2018), 22-26.

    ● Characteristic function of Cayley projective plane as a harmonic manifold (joint with Y. Euh and K. Sekigawa), Hokkaido Math J, 47 (2018) , 191-203.

    ● Moduli spaces of oriented Type A manifolds of dimension 3 (joint with P. Gilkey), J. Korean Math. Soc. (2017) 54 (6), 1759-1786.

    ● Characteristic function on symmetric Damek-Ricci space (joint with S. Kim), Bull. Korean Math. Soc. 2017 54 (3), 911-916.

    ● A curvature identity on a 6-dimensional Riemannian Manifolds and its applications (joint with Y. Euh and K. Sekigawa), Czech Math J. vol. 67, no. 1 (2017), 253-270.

    ● Euler-Lagrange formulas for pseudo-Kähler manifolds, J. Geom. physics 99 (2016), 239-243.
     ● Real analytic complete non-compact surfaces in R^n with finite total curvature arising as solutions to ODEs (joint with P. Gilkey and C. Kim), Tohoku Math J., 69 (1) (2017), 1-23.

    ● H-contact unit tangent sphere bundles of Riemannina manifolds (joint with Y. Nikolayevsky), Differ. Geom. Appl. 49 (2016), 301-311.

    ● Harmonic Hadamard manifolds of prescribed curvature and volume entropy (joint with Itoh, S. Kim, Satoh), Kyushu Journal of Mathematics Vol. 70 (2016) No. 2 267-280.

    ● Universal curvature identities and Euler-Lagrange formulas for Kähler manifolds, (Joint with Gilkey and Sekigawa), J. Math. Soc. Japan 68 (2016), 459–487.
    ● Euler-Lagrange formulas for pseudo-Kähler manifolds, J. Geom. physics 99 (2016) 239-243.
    ● Anti-invariant Riemannian Submersions, (Joint with P. Gilkey and M. Itoh) Twaiwanese J Math. (2016) 20 (4).
    ● Einstein conditions for the base space of anti-invariant Riemannian submersions and Clairaut submersions, (joint with J. Lee, B. Sahin and D. Song) Taiwanese J Math. 19 (4) (2015) 1145-1160.
    ● A curvature identity on a 6-dimensional Riemannian Manifolds and its applications, Czech Math J. 67 (2017), 253-270.
    ● Analytic continuation, the Chern-Gauss-Bonnet theorem, and the Euler-Lagrange equations in Lovelock theory for indefinite signature metrics , (joint with P. Gilkey), J. Geom. Phys., 88 (2015), 88-93.
    ● Curvature identities derived from the integral formula for the first Pontrjagin number , (joint with Y. Euh, and K. Sekigawa), Differ. Geom. Appl., 31 (4) (2013), 463-471.
    ● Universal curvature identities III  (joint with P. Gilkey, and K. Sekigawa), J. Geom. Methods Mod. Phys (IJGMMP), 10(6), 1350025.
    ● A curvature identity on a 4-dimensional Riemannian manifold , (joint with Y. Euh, and K. Sekigawa), Results in Mathematics 63 (1) (2013), 107-114.
    ● Spectral geometry of eta-Einstein Sasakian manifolds , J. Geom. Phys. 62 (2012), 2140–2146.
    ● Critical Hermitian structures on the product of Sasakian manifold , (joint with J. Lee and K. Sekigawa), J. Geom. Methods Mod. Phys (IJGMMP), 9 (7) (2012) 1250055 (16 pages).
    ● Notes on some classes of 3-dimensional contact metric manifolds , (joint with J. E. Jin, and K. Sekigawa), Balkan J. Geom. Appl. 17 (2) (2012) 42-53.
    ● Hermitian structures on the product of Sasakian manifolds , Geometriae Dedicata, 161 (2012), 399-408.
    ● Universal curvature identities II , (joint with P. Gilkey, and K. Sekigawa), J. Geom. Phys. 62 (2012) 814-825.
    ● A remark concerning universal curvature identities on 4-dimensional Riemannian manifolds , (joint with Y. Euh, and C. Jeong), Bull KMS. 49 (5) (2012), 1081-1088.
    ● Universal curvature identities , (joint with P. Gilkey, and K. Sekigawa), Differential Geom. Appl. 29 (2011), 770-778.
    ● A curvature identity on a 4-dimensional Riemannian manifold , (joint with Y. Euh, and K. Sekigawa), Results in Mathematics 63 (1) (2013), 107-114.
    ● Critical metrics for quadratic functionals in the curvature on 4-dimensional manifolds , (joint with Y. Euh, and K. Sekigawa) Differential Geom. Appl. 29 (2011), 642-646.
    ● A generalization of a 4-dimensional Einstein manifold (joint with Y. Euh and K. Sekigawa), Mathematica Slovaca. 63 (2013), 595-610.
    ● Some critical almost Hermitian structures (joint with J. Lee and K. Sekigawa), Results Math. Results in Mathematics, 63 (1) (2013), 31-45.
    ● H-contact unit tangent sphere bundles of four-dimensional Riemannian manifolds (joint with SH Chun and K. Sekigawa), J. Aust Math. Soc.  91 (2011), 243-256.
    ● H-contact unit tangent sphere bundles of Einstein manifolds (joint with SH Chun and K. Sekigawa), Quart. J. Math. 62  (2011), 59-69.
    ● A remark on H-contact unit tangent sphere bundles (joint with SH Chun, H. K. Pak and K. Sekigawa), J. Korean Math. Soc. 48 (2011), 363-375.
    ● Eta Einstein tangent sphere bundle with constant radii (joint with SH Chun and K. Sekigawa) Int. J. Geom. Methods Mod. Physics, 6 (2009), 965-984.
    ● When are the tangent sphere bundles of a Riemannian manifold eta-Einstein? , (joint with K. Sekigawa) Ann. Global Anal. Geom. 36 (2009), 275-284.
    ● Notes on tangent sphere bundles of constant radii , (joint with K. Sekigawa) J. Korean Math. Soc. 46 (2009), 1255-1265.
    ● Nearly Kaehler manifolds with vanishing Tricerri-Vanhecke Bochner curvature tensor (joint with Y. Euh, and K. Sekigawa), Differential Geom. Appl. 27 (2009), 250-256.
    ● Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series (joint with P. Gilkey, and C. Dunn) J. Phys. A: Math. Theor. 41 (2008) 135204 (4pp).
    ● Remarks on eta Einstein unit tangent bundle (joint with Y. Chai, S. Chun, and K. Sekigawa) Monatsh. Math. 155 (2008), 35-42.
    ● The spectral geometry of the canonical Riemannian submersion of a compact Lie Group (joint with P. Gilkey and C. Dunn ), J. Geom. Phys. 57 (2007), 2065-2076.
    ● Eigenforms of the Laplacian for Riemannian V-submersions (joint with P. Gilkey and H. Kim), Tohoku Math. J 57 (2005), 505-519.
    ● The Spectral Geometry of Einstein mainfolds with boundary , J. Korean Math. Soc. 41 (2004), 875-882.
    ● Heat Content asymptotics for operators of Laplace type with spectral boundary conditions (joint with P. Gilkey, K. Kirsten), Lett. Math. Phys. 68 (2004), 67-76.
    ● Spectral Geometry and the Kaehler Condition for Hermitian Manifolds with Boundary ,  Contemp. Math. Amer. Math. Soc   337 (2003), 121-128.
    ● Heat trace asymptotics of a time-dependent process (joint with P. Gilkey and K. Kirsten), J. Phys. A : Math. Gen. 34 (2001), 1153-1168.
    ● The spectral geometry of Riemannian submersions for manifolds with boundary , Rocky Mountain J. Math. 30 (2000), 353-369.
    ● Continuous variation of eigenvalues and Garding's inequality , Differential Geom. Appl. 10 (1999), 187-189.
    ● The Bochner Laplacian, Riemannian submersions, Heat content asymptotics and Heat equation asymptotics (joint with P.Gilkey), Czech Math J.49 (1999), 233-240.
    ● The eigenforms of the complex Laplacian for a Hermitian submersion (joint with P. Gilkey and J.Leahy), Nagoya Math. J. 156 (1999), 1-23.
    ● Eigenvalues of the form valued Laplacian for Riemannian submersions (joint with P. Gilkey and J. Leahy), Proc. Amer. Math. Soc. 126 (1998) , 1845-1850.
    ● Invariant metrics of positive Ricci curvature on principal bundles (joint with P.Gilkey and W.Tuschumann) , Math. Z. 227 (1998), 455-463.
    ● Eigenforms of the spin Laplacian and projectable spinors for principal bundles (joint with P. Gilkey and J. Leahy), Nuclear Physics B 514 (1998), 740-752.
    ● The spectral geometry of the Hopf fibration (joint with P. Gilkey and J. Leahy), J. Physics A 29 (1996), 5645-5656 .
    ● Riemannian submersions which perserve the eigenforms of the Laplacian (joint with P.Gilkey), Illinois J. Math. 40 (1996), 194-201.
    ● Eigen 1-forms of the Laplacian and Riemannian submersions , Bull. Korean Math. Soc. 33 (1996), 111-113.
    ● The Laplace-Beltrami operators and Riemannian submersions with minimal and not totally geodesic fibers , Bull. Korean Math. Soc. 27 (1990), 39-47.
    ● Transverse fields preserving the transverse Ricci field of a foliation (joint with S.Yorozu), J. Korean Math. Soc. 27 (1990), 167-175.

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⊙ 저서:

 

Aspects of Differential Geometry I (joint with P. Gilkey and R. Lorenzo), Morgan & Claypool Publishers, 2015. ISBN 978-1-62705-662-5.
Aspects of Differential Geometry II (joint with P. Gilkey and R. Lorenzo), Morgan & Claypool Publishers, 2015. ISBN 978-1-62705-783-7.

Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture(joint with P. Gilkey and J. Leahy), Studies in Advanced Mathematics, CRC Press (USA)1999 .
Spinors, Spectral Geometry, and Riemannian Submersions(joint with P. Gilkey and J. Leahy), Lecture Note Series 40, 서울대학교, 1998. See also EMIS Web Server .
누구나 할 수 있는 C프로그램 기초, 박정형 외 2인 (2005년 9월)
GSP를 이용한 기하 탐구, 박정형 외 2인, 경문사(2003년 3월)
재미있는 수학의 세계, 박정형 외 5인, 교우사(1999년 9월)
공업수학, 박정형 외 5인, 경문사(1997년 9월)
미적분학 박정형 외 4인 경문사(1997년 2월)
기타 2권

 

 

⊙ 주요 학술 활동:

 

● University of Oregon, Geometric Analysis Seminar (2020. 3. 10) – Harmonic manifolds

● AMSI/AustMS Workshop on Geometric Analysis and homogeneous Geometry, The University of Queensland, Brisbane Australia 24-28 June 2019 (invited) - Volume density function and submanifold of harmonic manifolds

The 7th Pacific RIM Conference on Mathematics, 서울대학교 (2016.6.27-7.1), 초청강연 - Universal Curvature Identities and their applications

한국 여성 수리과학회 대외협력이사 (2015.1.1-12.31)
ICM 2014 Satellite Conference on Geometric Analysis, 성균관대학교 (2014.8.22-24), 조직위원
Tokyo-Seoul Conference in Mathematics, University of Tokyo (2013.11.30-12.1), 초청강연
The Asian Mathematical conference (AMC) 2013, BEXCO (Busan Exhibition and Convention Center) (2013.6.30-7.4), 조직위원
NIMS Workshop : Hot Topics Workshop on Differential Geometry and Mathematical Physics (2013.2.18-21), 초청강연 - Universal curvature identity
KIAS Geometry seminar (2012.1.4) -The Universal curvature identity on a 4-dimensional Riemannian manifold and its application
한국 여성 수리과학회 International Conference for Women in Mathematics, 고등과학원 (2011.6.20-21), 조직위원
한국 여성 수리과학회 학술이사 (2008.6-2011.6) 
Conference in Geometry and Global Analysis, Santiago, Spain (2010.12.13-17) 초청강연 - Harmonic Characteristic vector fields on unit tangent sphere bundles
International workshop on differential geometry, 성균관대학교 (2010.6.25-26) 조직위원장
한국 여성 수리과학회 International Conference for Women in Mathematics, 충남대학교 (2010.6.21-22), 조직위원
2009 Joint meeting of the Korean Math. Soc. (KMS) and the American Math. Soc. (AMS), (2009.12.16-20) 스펙트럴 기하 분과 초청강연 - Harmonic Characteristic vector fields on unit tangent sphere bundles
카이스트 콜로퀴엄 (2009.9.4) - Recent work on unit tangent sphere bundles
2009 NIMS International Workshop on Differential Geometry and Related Topics, Jeju National University (2009.8.10-14) 초청강연
한국 여성 수리과학회 International Conference for Women in Mathematics, Korean Women in Mathematical Sciences (KWMS) (2009.6.19) 기하학 분과 초청강연 - TV Bochner flat almost Kahler surface
Korea-Australia Analysis Forum 2009 (KAAF 2009), BEXCO(Busan Exhibition and Convention Center) (2009.5.11-14) 초청강연

10th International Conference Differential Geometry and its Applications, Olomouc (Czech Republic)(2007. 8), 초청강연 - Spectral geometry of the Riemannian submersion of a compact Lie Group 
KIAS Summer School on Dirac and Laplace Operators, KIAS (2007.7.9-13), Organizer
KMS Global Day , 서울대학교 (2006. 10), 강연 - Canonical Riemannian submersion of compact Lie group
KIAS Workshop on Spectral Invariants and Related Topics , KIAS(2006. 5. 29-31), 초청강연 - Eta invariants with spectral boundary conditions
제 2회(2005), 제 4회(2007) 여성 수리과학회 국제 학술회의 조직위원 및 기하학 분과 위원장
● Geometry/Topology Seminar, University of Oregan(2003. 10), 초청강연 - Spectral geometry of Einstein manifolds with boundary
Dartmouth College(2003. 6), 초청강연 - The Spectral geometry of manifolds with boundary
AMS Special Session on Recent Advances in Riemannian and Lorenzian Geometries, Baltimore(2003. 1), 초청강연 - Spectral geometry of holomorphic manifolds with boundary
2002.10 - 현재 : 과학기술 앰배서더
2002.3.2 - 2002.7.5 : 제 22회 대우 국제 학술회의 조직위원장
International conference on Quamtum Gravity and Spectral Geometry, 논문발표(나폴리(이태리), 2001. 7)
Global Riemannian Geometry Workshop, 초청 강연 (KIAS, 2000. 1)
Conference on Differantial Geometry, 초청 강연 (북경대학교 , 1999. 8)
Pacific Northwest Geometry Seminar, 1997 Winter meeting 초청강연(MSRI(Berkeley)개최, 1997. 2) 발표.
대한 수학회 초청 강연 (단국대학교,2005.4)
호남수학회 학술상 수상 (1999. 6)
호남대학교 우수교원(학술상)표창 (1998. 6)
대한 수학회 초청 강연 (한남대학교,1998.4)외 35편 발표