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edit approved Jun 8, 2019 at 11:34
C.F.G
edit approved Jun 8, 2019 at 11:34
C.F.G
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X$X$ is an n$n$-dim positively curved manifold and Y$Y$ is a totally geodesic submanifold of codimension 1.Then Then cutting along Y$Y$ we get n$n$-dim positively curved manifolds without boundary,by by soul theorem these manifolds should be homeomorphic to R^n$\Bbb R^n$.Am Am I right?If not,please give counterexamples.

X is an n-dim positively curved manifold and Y is a totally geodesic submanifold of codimension 1.Then cutting along Y we get n-dim positively curved manifolds without boundary,by soul theorem these manifolds should be homeomorphic to R^n.Am I right?If not,please give counterexamples.

$X$ is an $n$-dim positively curved manifold and $Y$ is a totally geodesic submanifold of codimension 1. Then cutting along $Y$ we get $n$-dim positively curved manifolds without boundary, by soul theorem these manifolds should be homeomorphic to $\Bbb R^n$. Am I right?If not,please give counterexamples.

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Renato G. Bettiol
Renato G. Bettiol
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jiangsaiyin
jiangsaiyin
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a result of soul theorem,right?

X is an n-dim positively curved manifold and Y is a totally geodesic submanifold of codimension 1.Then cutting along Y we get n-dim positively curved manifolds without boundary,by soul theorem these manifolds should be homeomorphic to R^n.Am I right?If not,please give counterexamples.