*-Ricci solitons of real hypersurfaces in non-flat complex space forms

We prove that if a Sasakian metric is a ∗-Ricci Soliton, then it is either positive Sasakian, or null-Sasakian. Next, we prove that if a complete Sasakian metric is an almost gradient ∗-Ricci Solit...

∗-Ricci Soliton within the frame-work of Sasakian and (κ,μ)-contact manifold

We classify real hypersurfaces of complex projective space C P m , m ⩾ 3 , with D -recurrent structure Jacobi operator and apply this result to prove the non-existence of such hypersurfaces with recurrent structure Jacobi operator.

Real hypersurfaces in complex projective space with recurrent structure Jacobi operator

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.

Homogeneous hypersurfaces in complex hyperbolic spaces

Abstract In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g is a *-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a *-Ricci soliton, then we show that M is of constant sectional curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. Finally, we prove that if g is a gradient almost *-Ricci soliton, then either M is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of M. We verify our result by constructing examples for both *-Ricci soliton and gradient almost *-Ricci soliton.

∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds

We propose a new computer environment for mathematicians that can be set up easily and quickly.

KNOPPIX/Math: portable and distributable collection of mathematical software and free documents

Some real hypersurfaces of complex projective space

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On Three Dimensional Real Hypersurfaces in Complex Space Forms

It is known that there are no real hypersurfaces with parallel Ricci tensor in complex projective space Pn(C) equipped with the Kahler metric. We proved in a previous paper that there are no real hypersurfaces with recurrent Ricci tensor in Pn(C) and such that the structure vector Þeld of M is a principal curvature vector everywhere. In the present paper we showed that there are no real hypersurfaces M in complex space forms Mn(c) with recurrent Ricci tensor.

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Note on real hypersurfaces of complex space forms with recurrent Ricci tensor

A Lie hypersurface in the complex hyperbolic space is a homogeneous real hypersurface without focal submanifolds. The set of all Lie hypersurfaces in the complex hyperbolic space is bijective to a closed interval, which gives a deformation of homogeneous hypersurfaces from the ruled minimal one to the horosphere. In this paper, we study intrinsic geometry of Lie hypersurfaces, such as Ricci curvatures, scalar curvatures, and sectional curvatures.

Tatsuyoshi Hamada

Papers

KNOPPIX/Math: portable and distributable collection of mathematical software and free documents

Some real hypersurfaces of complex projective space

On Three Dimensional Real Hypersurfaces in Complex Space Forms

Note on real hypersurfaces of complex space forms with recurrent Ricci tensor

Curvature properties of Lie hypersurfaces in the complex hyperbolic space