Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 1, pp. 9-24 (2003)

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More on Convolution of Riemannian Manifolds

Bang-Yen Chen

Department of Mathematics, Michigan State University, East Lansing, MI 48824--1027, U.S.A. e-mail:

Abstract: In an earlier paper [1], the author introduced the notion of convolution of Riemannian manifolds. In [1] he also provided some examples and applications of convolution manifolds. In this paper we use tensor product to construct more examples of convolution manifolds and investigate fundamental properties of convolution manifolds. In particular, we study the relationship between convolution manifolds and the gradient of their scale functions. Moreover, we obtain a necessary and sufficient condition for a factor of a convolution Riemannian manifold to be totally geodesic. We also completely classify flat convolution Riemannian surfaces. \smallskip

[1] Chen, B. Y.: Convolution of Riemannian manifolds and its applications. To appear.

Keywords: convolution manifold, convolution Riemannian manifold, convolution metric, conic submanifold, totally geodesic submanifolds, flat convolution Riemannian surface, tensor product immersion

Classification (MSC2000): 53B20, 53C50; 53C42, 53C17

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Electronic version published on: 3 Apr 2003. This page was last modified: 4 May 2006.

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