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 $\small{h(=1/2L\xi\varphi)}$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $\small{L\xi}$ denote the Lie derivative in the characteristic direction $\small{\xi}$.
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
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Mok-Siu-Yeung type formulas on contact locally sub-symmetric spaces, Annals of Global Analysis and Geometry, 2009, 35, 1, 1
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Pseudo-Hermitian symmetries, Israel Journal of Mathematics, 2008, 166, 1, 125
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A CLASSIFICATION OF SPHERICAL SYMMETRIC CR MANIFOLDS, Bulletin of the Australian Mathematical Society, 2009, 80, 02, 251
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PSEUDOHERMITIAN LEGENDRE SURFACES OF SASAKIAN SPACE FORMS, Communications of the Korean Mathematical Society, 2015, 30, 4, 457
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SLANT CURVES IN CONTACT PSEUDO-HERMITIAN 3-MANIFOLDS, Bulletin of the Australian Mathematical Society, 2008, 78, 03, 383
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A Schur-type theorem for CR-integrable almost Kenmotsu manifolds, Mathematica Slovaca, 2016, 66, 5
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