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Harmonic manifolds with some specific volume densities

DSpace at IIT Bombay

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Title Harmonic manifolds with some specific volume densities
 
Creator RAMACHANDRAN, K
RANJAN, A
 
Subject harmonic manifolds
volume densities
ricci curvature
second fundamental form
 
Description We show that a noncompact, complete, simply connected harmonic manifold (M-d,g) with volume density theta(m)(r) = sinh(d-1) r is isometric to the real hyperbolic space and a noncompact, complete, simply connected Kahler harmonic manifold (M-2d,g) with volume density theta(m)(1)= sinh(2d-1) r cosh r is isometric to the complex hyperbolic space. A similar result is also proved for quaternionic Kahler manifolds. Using our methods we get an alternative proof, without appealing to the powerful Cheeger-Gromoll splitting theorem, of the fact that every Ricci flat harmonic manifold is Rat. Finally a rigidity result for real hyperbolic space is presented.
 
Publisher INDIAN ACADEMY SCIENCES
 
Date 2011-08-02T03:51:56Z
2011-12-26T12:53:40Z
2011-12-27T05:40:29Z
2011-08-02T03:51:56Z
2011-12-26T12:53:40Z
2011-12-27T05:40:29Z
1997
 
Type Article
 
Identifier PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 107(3), 251-261
0253-4142
http://dx.doi.org/10.1007/BF02867256
http://dspace.library.iitb.ac.in/xmlui/handle/10054/8648
http://hdl.handle.net/10054/8648
 
Language en