Journal of Differential Geometry

Taut submanifolds and foliations

Stephan Wiesendorf

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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 $\mathbb{Z}_2$-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 $\mathbb{Z}_2$-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.

Article information

Source
J. Differential Geom., Volume 96, Number 3 (2014), 457-505.

Dates
First available in Project Euclid: 20 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1395321847

Digital Object Identifier
doi:10.4310/jdg/1395321847

Mathematical Reviews number (MathSciNet)
MR3189462

Zentralblatt MATH identifier
1302.53032

Citation

Wiesendorf, Stephan. Taut submanifolds and foliations. J. Differential Geom. 96 (2014), no. 3, 457--505. doi:10.4310/jdg/1395321847. https://projecteuclid.org/euclid.jdg/1395321847


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