More on Convolution of Riemannian Manifolds Dedicated to Professor T. Otsuki on his eighty-fifth birthday
نویسنده
چکیده
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. MSC 2000: 53B20, 53C50 (primary); 53C42, 53C17 (secondary)
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