• 대한수학회보
• /
• 제40권3호
• /
• pp.457-464
• /
• 2003

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.

• 대한수학회논문집
• /
• 제18권3호
• /
• pp.501-513
• /
• 2003

The Matsumoto metric is an ($\alpha,\;\bata$)-metric which is an exact formulation of the model of Finsler space. Lately, this metric was expressed as an infinite series form for $$\mid$\beat$\mid$\;<\;$\mid$\alpha$\mid$$ by the first author. He introduced an approximate Matsumoto metric as the ($\alpha,\;\bata$)-metric of finite series form and investigated it in [11]. The purpose of the present paper is devoted to finding the condition for a Finsler space with an approximate Matsumoto metric to be projectively flat.

• East Asian mathematical journal
• /
• 제27권5호
• /
• pp.557-564
• /
• 2011

In 2007, Huang and Zhang [1] introduced a cone metric space with a cone metric generalizing the usual metric space by replacing the real numbers with Banach space ordered by the cone. They considered some fixed point theorems for contractive mappings in cone metric spaces. Since then, the fixed point theory for mappings in cone metric spaces has become a subject of interest in [1-6] and references therein. In this paper, we consider some fixed point theorems for generalized nonexpansive setvalued mappings under suitable conditions in sequentially compact cone metric spaces and complete cone metric spaces.

• Structural Engineering and Mechanics
• /
• 제17권6호
• /
• pp.767-788
• /
• 2004

The classical 8-node isoparametric serendipity element uses parametric shape functions for both test and trial functions. Although this element performs well in general, it yields poor results under severe mesh distortions. The distortion sensitivity is caused by the lack of continuity and/or completeness of shape functions used for test and trial functions. A recent element using parametric and metric shape functions for constructing the test and trial functions exhibits distortion immunity. This paper discusses the choice of parametric or metric shape functions as the basis for test and/or trial functions, satisfaction of continuity and completeness requirements, and their connection to distortion sensitivity. Also, the performances of four types of elements, viz., parametric, metric, parametric-metric, and metric-parametric, are compared for distorted meshes, and their merits and demerits are discussed.

• Kyungpook Mathematical Journal
• /
• 제59권1호
• /
• pp.163-174
• /
• 2019

The object of this paper is to classify paracontact metric ($k,{\mu}$)-spaces satisfying certain curvature conditions. We show that a paracontact metric ($k,{\mu}$)-space is Ricci semisymmetric if and only if the metric is Einstein, provided k < -1. Also we prove that a paracontact metric ($k,{\mu}$)-space is ${\phi}$-Ricci symmetric if and only if the metric is Einstein, provided $k{\neq}0$, -1. Moreover, we show that in a paracontact metric ($k,{\mu}$)-space with k < -1, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor. Several consequences of these results are discussed.

• 대한수학회논문집
• /
• 제37권3호
• /
• pp.825-837
• /
• 2022

We characterize a three-dimensional Riemannian manifold endowed with a type of semi-symmetric metric P-connection. At first, it is proven that if the metric of such a manifold is a gradient m-quasi-Einstein metric, then either the gradient of the potential function 𝜓 is collinear with the vector field P or, λ = -(m + 2) and the manifold is of constant sectional curvature -1, provided P𝜓 ≠ m. Next, it is shown that if the metric of the manifold under consideration is a gradient 𝜌-Einstein soliton, then the gradient of the potential function is collinear with the vector field P. Also, we prove that if the metric of a 3-dimensional manifold with semi-symmetric metric P-connection is a gradient 𝜔-Ricci soliton, then the manifold is of constant sectional curvature -1 and λ + 𝜇 = -2. Finally, we consider an example to verify our results.

• Nonlinear Functional Analysis and Applications
• /
• 제27권2호
• /
• pp.289-308
• /
• 2022

In this paper, we introduce the concept of M^*-metric spaces and how much the M^*-metric and the b-metric spaces are related. Moreover, we introduce some ways of generating M^*-metric spaces. Also, we investigate some types of convergence associated with M^*-metric spaces. Some common fixed point for contraction and generalized contraction mappings in M^*-metric spaces. Our work has been supported by many examples and an application.

• 대한수학회논문집
• /
• 제11권2호
• /
• pp.407-413
• /
• 1996

The $(\alpha, \beta)$-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-form $\Beta$; it has been sometimes treat in theoretical physics. In particular, the projective flatness of Finsler space with a metric $L^2 = 2\alpha\beta$ is considered in detail.

• Korean Journal of Mathematics
• /
• 제4권2호
• /
• pp.117-124
• /
• 1996

In this paper we define a new fuzzy metric $\tilde{\theta}$ of fuzzy number sequences, and prove that the space of convergent sequences of fuzzy numbers is a fuzzy complete metric space in the fuzzy metric $\tilde{\theta}$.

• 호남수학학술지
• /
• 제36권4호
• /
• pp.853-862
• /
• 2014

In this paper, we define a metric induced by the Bergman Kernel and prove a property that the metric has under any biholomorphic mapping.