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Convexity of spheres in a manifold without conjugate points

DSpace at IIT Bombay

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Title Convexity of spheres in a manifold without conjugate points
 
Creator RANJAN, A
SHAH, H
 
Subject spaces
index lemma
minimal horospheres
vector bundle
stiefel-whitney classes
focal set
 
Description For a non-compact, complete and simply connected manifold M without conjugate points, we prove that if the determinant of the second fundamental form of the geodesic spheres in M is a radial function, then the geodesic spheres are convex. We also show that if M is two or three dimensional and without conjugate points, then, at every point there exists a ray with no focal points on it relative to the initial point of the ray. The proofs use a result from the theory of vector bundles combined with the index lemma.
 
Publisher INDIAN ACADEMY SCIENCES
 
Date 2011-08-02T01:51:06Z
2011-12-26T12:53:37Z
2011-12-27T05:40:13Z
2011-08-02T01:51:06Z
2011-12-26T12:53:37Z
2011-12-27T05:40:13Z
2002
 
Type Article
 
Identifier PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 112(4), 595-599
0253-4142
http://dx.doi.org/10.1007/BF02829692
http://dspace.library.iitb.ac.in/xmlui/handle/10054/8615
http://hdl.handle.net/10054/8615
 
Language en