• 대한수학회논문집
• /
• 제31권1호
• /
• pp.163-176
• /
• 2016

The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, ${\mu}$)-contact metric manifolds.

• 대한수학회지
• /
• 제40권1호
• /
• pp.129-167
• /
• 2003

In this paper we introduce new notions of Ricci-like tensor and many kind of curvature-like tensors such that concircular, projective, or conformal curvature-like tensors defined on semi-Riemannian manifolds. Moreover, we give some geometric conditions which are equivalent to the Codazzi tensor, the Weyl tensor, or the second Bianchi identity concerned with such kind of curvature-like tensors respectively and also give a generalization of Weyl's Theorem given in [18] and [19].

• 대한수학회보
• /
• 제33권3호
• /
• pp.455-463
• /
• 1996

In [3] and [4], Kitahara, Pak and the author obtained the conformally invariant tensor $B_0$, which is an algebraic Hermitian analogue of the Weyl conformal curvature tensor W in the Riemannian geometry, by the decomposition of the curvature tensor H of the Hermitian connection and the notion of semi-curvature-like tensors of Tanno (see[7]). In [5], the author defined a conformally invariant tensor $B_0$ on a Hermitian manifold as a modification of $B_0$. Moreover he introduced the notion of local conformal Hermitian-flatness of Hermitian manifolds and proved that the vanishing of this tensor $B_0$ together with some condition for the scalar curvatures is a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat.

• Kyungpook Mathematical Journal
• /
• 제60권4호
• /
• pp.805-819
• /
• 2020

The objective of this study is to investigate 𝜂-Einstein solitons on (𝜀)-Kenmotsu manifolds when the Weyl-conformal curvature tensor satisfies some geometric properties such as being flat, semi-symmetric and Einstein semi-symmetric. Here, we discuss the properties of 𝜂-Einstein solitons on 𝜑-symmetric (𝜀)-Kenmotsu manifolds.

• 대한수학회논문집
• /
• 제22권3호
• /
• pp.411-417
• /
• 2007

N(k)-quasi Einstein manifolds are introduced and studied.

• 대한수학회논문집
• /
• 제36권4호
• /
• pp.771-782
• /
• 2021

In this paper we introduce generalized weakly semi-conformally symmetric manifold, a generalization of weakly symmetric manifold. We study some basic properties and obtain the forms of the scalar curvature of such manifold. In the last section an example is given to ensure the existence of such manifold.