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Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition

Hyunjin Lee, Seonhui Kim, Young Jin Suh (2012)

Czechoslovak Mathematical Journal

In this paper, first we introduce a new notion of commuting condition that φ φ 1 A = A φ 1 φ between the shape operator A and the structure tensors φ and φ 1 for real hypersurfaces in G 2 ( ℂ m + 2 ) . Suprisingly, real hypersurfaces of type ( A ) , that is, a tube over a totally geodesic G 2 ( ℂ m + 1 ) in complex two plane Grassmannians G 2 ( ℂ m + 2 ) satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in G 2 ( ℂ m + 2 ) satisfying the commuting condition. Finally we get a characterization of Type ( A ) in terms of such commuting...

Real hypersurfaces with constant totally real bisectional curvature in complex space forms

Miguel Ortega, Juan de Dios Pérez, Young Jin Suh (2006)

Czechoslovak Mathematical Journal

In this paper we classify real hypersurfaces with constant totally real bisectional curvature in a non flat complex space form M m ( c ) , c ≠ 0 as those which have constant holomorphic sectional curvature given in [6] and [13] or constant totally real sectional curvature given in [11].

Reflections with respect to submanifolds in contact geometry

P. Bueken, Lieven Vanhecke (1993)

Archivum Mathematicum

We study to what extent some structure-preserving properties of the geodesic reflection with respect to a submanifold of an almost contact manifold influence the geometry of the submanifold and of the ambient space.

Regular and biregular functions in the sense of Fueter - some problems

W. Królikowski, R. Michael Porter (1994)

Annales Polonici Mathematici

The biregular functions in the sense of Fueter are investigated. In particular, the class of LR-biregular mappings (left regular with a right regular inverse) is introduced. Moreover, the existence of non-affine biregular mappings is established via examples. Some applications to the quaternionic manifolds are given.

Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form

Esmaeil Abedi, Reyhane Bahrami Ziabari, Mukut Mani Tripathi (2016)

Archivum Mathematicum

We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, θ -slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.

Ricci curvature of real hypersurfaces in complex hyperbolic space

Bang-Yen Chen (2002)

Archivum Mathematicum

First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.

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