Gabjin Yun

CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold M. We prove that if the criti- cal point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an n-dimensional Rie- mannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.

Fuzzy Lipschitz maps and fixed point theorems in fuzzy metric spaces

In this paper, we introduce the notion of dilation and fuzzy Lipschitz of a map from a fuzzy metric space into a fuzzy metric space and we prove continuity properties for such maps. We also define the notion of the fuzzy Lipschitz distance between two fuzzy metric spaces and show that two compact fuzzy metric spaces whose Lipschitz distance is zero is fuzzy isometric to each other. On the other hand, we introduce the concept of minimal slope of a map between fuzzy metric spaces, which is defined by the ratio of two fuzzy metrics and derive some properties on it and relations with the dilation. In particular, we show that if the dilation of a map from a fuzzy metric space which is complete in George and Veeramani sense into itself is less than the minimal slope, then the map must have a fixed point. In case that a fuzzy metric space is considered in the sense of Kramosil and Michalek and that the completeness in the sense of Grabiec, the same result holds.

Bach-flat h-almost gradient Ricci solitons

On an

STRUCTURE OF STABLE MINIMAL HYPERSURFACES IN A RIEMANNIAN MANIFOLD OF NONNEGATIVE RICCI CURVATURE

n

ON THE STRUCTURE OF MINIMAL SUBMANIFOLDS IN A RIEMANNIAN MANIFOLD OF NON-NEGATIVE CURVATURE

-dimensional complete manifold

TOTAL SCALAR CURVATURE AND HARMONIC CURVATURE

M

Rigidity of the critical point equation

, consider an

Erratum to: Total Scalar Curvature and Harmonic Curvature

h

Nonexistence of multiple black holes in static space-times and weakly harmonic curvature

-almost gradient Ricci soliton, which is a generalization of a gradient Ricci soliton. We prove that if the manifold is Bach-flat and

WEAKLY EINSTEIN CRITICAL POINT EQUATION

dh/du>0