Ruled real hypersurfaces of complex space forms

We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous example in the complex hyperbolic space.

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A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

Mathematics ◽

10.3390/math8040642 ◽

2020 ◽

Vol 8 (4) ◽

pp. 642

Author(s):

George Kaimakamis ◽

Konstantina Panagiotidou ◽

Juan de Dios Pérez

Keyword(s):

Ricci Tensor ◽

Complex Space ◽

Space Form ◽

Flat Space ◽

Real Hypersurfaces ◽

Space Forms ◽

Ruled Real Hypersurfaces ◽

Levi Civita Connection ◽

Complex Space Forms

The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface M in a non-flat complex space form. For any nonnull constant k and any vector field X tangent to M the k-th Cho operator F X ( k ) is defined and is related to both connections. If X belongs to the maximal holomorphic distribution D on M, the corresponding operator does not depend on k and is denoted by F X and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that F X S = S F X , where S denotes the Ricci tensor of M and a further condition is satisfied, are classified.

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Real hypersurfaces of complex space forms satisfying Fischer–Marsden equation

ANNALI DELL UNIVERSITA DI FERRARA ◽

10.1007/s11565-021-00361-x ◽

2021 ◽

Author(s):

V. Venkatesha ◽

Devaraja Mallesha Naik ◽

H. Aruna Kumara

Keyword(s):

Complex Space ◽

Real Hypersurfaces ◽

Space Forms ◽

Complex Space Forms

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Some new results on real hypersurfaces with generalized Tanaka-Webster connection

Mathematica Slovaca ◽

10.1515/ms-2017-0255 ◽

2019 ◽

Vol 69 (3) ◽

pp. 665-674

Author(s):

Wenjie Wang ◽

Ximin Liu

Keyword(s):

Real Hypersurface ◽

Complex Space ◽

Shape Operator ◽

Real Hypersurfaces ◽

Space Forms ◽

Complex Dimension ◽

Nonflat Complex Space Forms ◽

Complex Space Forms ◽

Ruled Real Hypersurface

Abstract Let M be a real hypersurface in nonflat complex space forms of complex dimension two. In this paper, we prove that the shape operator of M is transversally Killing with respect to the generalized Tanaka-Webster connection if and only if M is locally congruent to a type (A) or (B) real hypersurface. We also prove that shape operator of M commutes with Cho operator on holomorphic distribution if and only if M is locally congruent to a ruled real hypersurface.

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REAL HYPERSURFACES IN NON-FLAT COMPLEX SPACE FORMS CONCERNED WITH THE STRUCTURE JACOBI OPERATOR AND RICCI TENSOR

Topics in Almost Hermitian Geometry and Related Fields ◽

10.1142/9789812701701_0011 ◽

2005 ◽

Author(s):

U-HANG KI ◽

SETSUO NAGAI ◽

RYOICHI TAKAGI

Keyword(s):

Ricci Tensor ◽

Complex Space ◽

Jacobi Operator ◽

Real Hypersurfaces ◽

Space Forms ◽

Structure Jacobi Operator ◽

Complex Space Forms

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On a New type of Tensor on Real Hypersurfaces in Non-Flat Complex Space Forms

Symmetry ◽

10.3390/sym11040559 ◽

2019 ◽

Vol 11 (4) ◽

pp. 559

Author(s):

George Kaimakamis ◽

Konstantina Panagiotidou

Keyword(s):

Curvature Tensor ◽

Complex Space ◽

Three Dimensional ◽

Real Hypersurfaces ◽

Weyl Curvature ◽

Space Forms ◽

Hopf Hypersurfaces ◽

Weyl Curvature Tensor ◽

New Type ◽

Complex Space Forms

In this paper the notion of ∗ -Weyl curvature tensor on real hypersurfaces in non-flat complex space forms is introduced. It is related to the ∗ -Ricci tensor of a real hypersurface. The aim of this paper is to provide two classification theorems concerning real hypersurfaces in non-flat complex space forms in terms of ∗ -Weyl curvature tensor. More precisely, Hopf hypersurfaces of dimension greater or equal to three in non-flat complex space forms with vanishing ∗ -Weyl curvature tensor are classified. Next, all three dimensional real hypersurfaces in non-flat complex space forms, whose ∗ -Weyl curvature tensor vanishes identically are classified. The used methods are based on tools from differential geometry and solving systems of differential equations.

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