GEOMETRY OF CONTACT STRONGLY PSEUDO-CONVEX CR-MANIFOLDS

Title & Authors
GEOMETRY OF CONTACT STRONGLY PSEUDO-CONVEX CR-MANIFOLDS
Cho, Jong-Taek;

Abstract
As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $\small{(M,\;\eta,\;\varphi)}$ with the pseudo-parallel structure operator $h( Keywords contact strongly pseudo-convex CR-manifold;Sasakian space form;contact strongly pseudo-convex CR-space form; Language English Cited by 1. PSEUDOHERMITIAN LEGENDRE SURFACES OF SASAKIAN SPACE FORMS,; 대한수학회논문집, 2015. vol.30. 4, pp.457-469 1. Mok-Siu-Yeung type formulas on contact locally sub-symmetric spaces, Annals of Global Analysis and Geometry, 2009, 35, 1, 1 2. Affine biharmonic submanifolds in 3-dimensional pseudo-Hermitian geometry, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2009, 79, 1, 113 3. Pseudo-Hermitian symmetries, Israel Journal of Mathematics, 2008, 166, 1, 125 4. A CLASSIFICATION OF SPHERICAL SYMMETRIC CR MANIFOLDS, Bulletin of the Australian Mathematical Society, 2009, 80, 02, 251 5. PSEUDOHERMITIAN LEGENDRE SURFACES OF SASAKIAN SPACE FORMS, Communications of the Korean Mathematical Society, 2015, 30, 4, 457 6. SLANT CURVES IN CONTACT PSEUDO-HERMITIAN 3-MANIFOLDS, Bulletin of the Australian Mathematical Society, 2008, 78, 03, 383 7. A Schur-type theorem for CR-integrable almost Kenmotsu manifolds, Mathematica Slovaca, 2016, 66, 5 8. Pseudo-Einstein manifolds, Topology and its Applications, 2015, 196, 398 References 1. E. Barletta and S. Dragomir, Differential equations on contact Riemannian manifolds, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4) 30 (2001), no. 1, 63-95 2. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Pro- gress in Mathematics 203, Birkhauser Boston, Inc., Boston, MA, 2002 3. D. E. Blair, T. Koufogiorgos, and B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 (1995), 189-214 4. E. Boeckx, A class of locally${\varphi}$-symmetric contact metric spaces, Arch. Math. (Basel) 72 (1999), no. 6, 466-472 5. E. Boeckx, A full classification of contact metric$({\kappa},{\mu})$-spaces, Illinois J. Math. 44 (2000), no. 1, 212-219 6. E. Boeckx and J. T. Cho,${\eta}$-parallel contact metric spaces, Differential Geom. Appl. 22 (2005), no. 3, 275-285 7. E. Boeckx and L. Vanhecke, Characteristic reflections on unit tangent sphere bundles, Houston J. Math. 23 (1997), no. 3, 427-448 8. J. T. Cho, A class of contact Riemannian manifolds whose associated CR- structures are integrable, Publ. Math. Debrecen 63 (2003), no. 1-2, 193-211 9. J. T. Cho and L. Vanhecke, Classification of symmetric-like contact metric$({\kappa},{\mu})$-spaces, Publ. Math. Debrecen 62 (2003), no. 3-4, 337-349 10. J. T. Cho and S. H. Chun, The unit tangent sphere bundle of a complex space form, J. Korean Math. Soc. 41 (2004), no. 6, 1035-1047 11. J. T. Cho and J. Inoguchi, Pseudo-symmetric contact 3-manifolds, J. Korean Math. Soc. 42 (2005), no. 5, 913-932 12. S. Ianus, Sulle varieta di Cauchy-Riemann, Rend. Accad. Sci. Fis. Mat. Napoli (4) 39 (1972), 191-195 13. S. Sasaki and Y. Hatakeyama, On differentiable manifolds with certain struc- tures which are closely related to almost contact structure II, Tohoku Math. J. 13 (1961), 281-294 14. N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Car- tan connections, Japan J. Math. (N.S.) 2 (1976), no. 1, 131-190 15. S. Tanno, The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700-717 16. S. Tanno, Sasakian manifolds with constant${\varphi}\$-holomororphic sectional curvature, Tohoku Math. J. (2) 21 (1969), 501-507

17.
S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), no. 1, 349-379

18.
S. Tanno, The standard CR structure on the unit tangent sphere bundle, Tohoku Math. J. (2) 44 (1992), no. 4, 535-543

19.
Y. Tashiro, On contact structures of tangent sphere bundles, Tohoku Math. J. (2) 21 (1969), 117-143

20.
S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), no. 1, 25-41