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Title: Fiberwise volume non-increasing diffeomorphisms on product manifolds
Authors: Dreesen, Dennis *
Petrosyan, Nansen * # ×
Issue Date: Dec-2010
Publisher: D. Reidel Pub. Co.
Series Title: Geometriae Dedicata vol:149 issue:1 pages:417-424
Abstract: Given a closed connected Riemannian manifold M and a connected Riemannian manifold N, we consider fiberwise, i.e. M x {z}, z is an element of N, volume non-increasing diffeomorphisms on the product M x N. Our main theorems show that in the presence of a certain cohomological condition on M and N such diffeomorphisms must map a fiber diffeomorphically onto another fiber and are therefore fiberwise volume preserving. As a first corollary, we show that the isometries of M x N split. As a second corollary, we prove a special case of an extension of Talelli's conjecture.
ISSN: 0046-5755
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Mathematics, Campus Kulak Kortrijk
* (joint) first author
× corresponding author
# (joint) last author

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