Universität zu Köln

Wiesendorf, Stephan (2014). TAUT SUBMANIFOLDS AND FOLIATIONS. J. Differ. Geom., 96 (3). S. 457 - 506. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1945-743X

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Abstract

We give an equivalent description of taut submanifolds of complete Riemannian manifolds as exactly those submanifolds whose normal exponential map has the property that every preimage of a point is a union of submanifolds. It turns out that every taut submanifold is also Z(2)-taut. We explicitly construct generalized Bott-Samelson cycles for the critical points of the energy functionals on the path spaces of a taut submanifold that, generically, represent a basis for the Z(2)-cohomology. We also consider singular Riemannian foliations all of whose leaves are taut. Using our characterization of taut submanifolds, we are able to show that tautness of a singular Riemannian foliation is actually a property of the quotient.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Wiesendorf, Stephan UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-444024
Journal or Publication Title:	J. Differ. Geom.
Volume:	96
Number:	3
Page Range:	S. 457 - 506
Date:	2014
Publisher:	INT PRESS BOSTON, INC
Place of Publication:	SOMERVILLE
ISSN:	1945-743X
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SPACES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/44402