Metrics on products of surfaces with non-positive sectional curvature

Perdomo O

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Metrics on products of surfaces with non-positive sectional curvature

机译：具有非正截面曲率的曲面的乘积的度量

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Let (Si, gi), i = 1, 2 be two compact riemannian surfaces isometrically embedded in euclidean spaces. In this paper we show that if M = S-1 x S-2, then for any function F: M -> R, the graph of F, i.e. the manifold { (x, F(x)) : x epsilon M}, does not have positive sectional curvature.

机译：令（Si，gi），i = 1，2是两个紧凑的黎曼曲面，它们等距地嵌入欧氏空间。在本文中，我们证明如果M = S-1 x S-2，则对于任何函数F：M-> R，F的图，即流形{（x，F（x））：x epsilon M} ，没有正的截面曲率。

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《Israel Journal of Mathematics》 |2006年第0期|共7页
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Perdomo O;
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正文语种 eng
中图分类数学;
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Metrics on products of surfaces with non-positive sectional curvature

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