Real Hypersurfaces in Complex Space Forms With etta-Parallel
Differential geometry of indefinite complex submanifolds in indefinite complex space forms.
On real hypersurfaces in quaternionic projective space with -recurrent second fundamental tensor.
Real hypersurfaces of type in quaternionic projective space.
Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator
In this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassmannians SU2.m/S(U2·Um), m≥3, whose structure tensors {ɸi}i=1,2,3 commute with the shape operator.
Real hypersurfaces in a complex projective space with pseudo--parallel structure Jacobi operator
We introduce the new notion of pseudo--parallel real hypersurfaces in a complex projective space as real hypersurfaces satisfying a condition about the covariant derivative of the structure Jacobi operator in any direction of the maximal holomorphic distribution. This condition generalizes parallelness of the structure Jacobi operator. We classify this type of real hypersurfaces.
Integral formulas for closed spacelike hypersurfaces in anti-de Sitter space
In this paper, we study closed -maximal spacelike hypersurfaces in anti-de Sitter space with two distinct principal curvatures and give some integral formulas about these hypersurfaces.
Real hypersurfaces with constant totally real bisectional curvature in complex space forms
In this paper we classify real hypersurfaces with constant totally real bisectional curvature in a non flat complex space form , as those which have constant holomorphic sectional curvature given in [6] and [13] or constant totally real sectional curvature given in [11].
Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians
We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian . In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in satisfying such conditions.
Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II
Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces of Type in complex two plane Grassmannians with a commuting condition between the shape operator and the structure tensors and for in . Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator and a new operator induced by two structure tensors and . That is, this commuting shape operator is given by . Using this condition, we prove that...
Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition
In this paper, first we introduce a new notion of commuting condition that between the shape operator and the structure tensors and for real hypersurfaces in . Suprisingly, real hypersurfaces of type , that is, a tube over a totally geodesic in complex two plane Grassmannians satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in satisfying the commuting condition. Finally we get a characterization of Type in terms of such commuting...
Real hypersurfaces in complex space forms concerned with the local symmetry
This paper consists of two parts. In the first, we find some geometric conditions derived from the local symmetry of the inverse image by the Hopf fibration of a real hypersurface in complex space form . In the second, we give a complete classification of real hypersurfaces in which satisfy the above geometric facts.
Real hypersurfaces with constant totally real sectional curvature in a complex space form
We characterize real hypersurfaces with constant holomorphic sectional curvature of a non flat complex space form as the ones which have constant totally real sectional curvature.
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