*-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

It is known that there are no Einstein real hypersurfaces in complex space forms equipped
 with the K\"ahler metric. In the present paper we classified the $*$-Einstein real
 hypersurfaces $M$ in complex space forms $M_{n}(c)$ and such that the structure vector is
 a principal curvature vector.

https://projecteuclid.org/download/pdf_1/euclid.tjm/1244208866

Real Hypersurfaces of Complex Space Forms in Terms of Ricci $*$-Tensor

Let M be a real hypersurface of the complex projective space
 Pn(C). The Ricci tensor S
 of M is recurrent if there exists a 1-form such that . In this paper we show that there
 are no real hypersurfaces with recurrent Ricci tensor of
 Pn(C) under the condition that is a principal curvature vector.1991 Mathematics
 Subject Classification 53C40
 (53C25).

/pdf/on-real-hypersurfaces-of-a-complex-projective-space-with-54gnxojiol.pdf

On real hypersurfaces of a complex projective space with recurrent Ricci tensor

/pdf/ruled-real-hypersurfaces-of-complex-space-forms-flrnpfibme.pdf

Ruled real hypersurfaces of complex space forms

KNOPPIX/Math offers many documents and mathematical software packages. Once you run the live system, you can enjoy a wonderful world of mathematical software without needing to install anything yourself. We will demonstrate how to boot and use this system.

Tatsuyoshi Hamada

Papers

Real Hypersurfaces of Complex Space Forms in Terms of Ricci $*$-Tensor

On real hypersurfaces of a complex projective space with recurrent Ricci tensor

Ruled real hypersurfaces of complex space forms

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Real hypersurfaces of complex space forms with symmetric Ricci *-tensor