Minimality of totally geodesic submanifolds in Finsler geometry
csal
- Berck, Gautier Département de Mathématiques, Université de Fribourg, 23, Chemin du Musée, 1700, Fribourg, Switzerland
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2009
Published in:
- Mathematische Annalen. - Springer-Verlag. - 2009, vol. 343, no. 4, p. 955-973
English
Using the symplectic definition of the Holmes-Thompson volume we prove that totally geodesic submanifolds of a Finsler manifold are minimal for this volume. Thanks to well suited technics the minimality of totally geodesic hypersurfaces (see Álvarez Paiva and Berck in Adv Math 204(2):647-663, 2006) and 2-dimensional totally geodesic surfaces (see Álvarez Paiva and Berck in Adv Math 204(2):647-663, 2006, Ivanov in Algebra i Analiz 13(1)26-38, 2001) had already been proved. However the corresponding statement for the Hausdorff measure is known to be wrong even in the simplest case of totally geodesic 2-dimensional surfaces in a 3-dimensional Finsler manifold (see Álvarez Paiva and Berck in Adv Math 204(2):647-663, 2006)
- Collections
- Language
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- English
- Classification
- Mathematics
- License
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License undefinedSpringer-Verlag, 2008
- Identifiers
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- RERO DOC 310329
- SWISSBIB (NATIONALLICENCE)springer-10.1007/s00208-008-0299-z
- DOI 10.1007/s00208-008-0299-z
- Persistent URL
- https://sonar.ch/global/documents/306594
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