Korean

⊙ 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.

2.  

⊙ 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