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Author

Tatsuyoshi Hamada

Other affiliations: Nihon University
Bio: Tatsuyoshi Hamada is an academic researcher from Fukuoka University. The author has contributed to research in topics: Ricci curvature & Mathematical software. The author has an hindex of 5, co-authored 17 publications receiving 124 citations. Previous affiliations of Tatsuyoshi Hamada include Nihon University.

Papers
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TL;DR: In this article, the authors classified the $*$-Einstein real hypersurfaces in complex space forms such that the structure vector is a principal curvature vector and the principal curvatures of the hypersurface can be computed with the K\"ahler metric.
Abstract: 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.

76 citations

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TL;DR: In this article, it was shown that there are no real hypersurfaces with recurrent Ricci tensors of the complex projective space Pn(C) under the condition that there is a principal curvature vector.
Abstract: 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).

17 citations

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TL;DR: This tutorial demonstrates how to boot and use the KNOPPIX/Math system, a wonderful world of mathematical software without needing to install anything yourself.
Abstract: 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.

7 citations


Cited by
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Journal ArticleDOI
TL;DR: In this paper, the notion of *-Ricci soliton is introduced and real hypersurfaces in non-flat complex space forms admitting a *-ricci s soliton with potential vector field being the structure vector field.

53 citations

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TL;DR: In this article, it was shown that if a complete Sasakian metric is an almost gradient ∗-Ricci soliton, then it is either positive or null-Sakian.
Abstract: 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...

37 citations

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TL;DR: In this paper, the authors 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 hypersurface with recurrent structure JacobI operator.
Abstract: 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.

32 citations

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TL;DR: In this paper, the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces is studied and a characterization of the focal set in terms of its second fundamental form is provided.
Abstract: 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.

29 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the case of *-Ricci soliton in the framework of a Kenmotsu manifold and proved that soliton constant λ is zero.
Abstract: 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.

29 citations