Integral formulae for a Riemannian manifold with two orthogonal distributions

• Autorzy: Vladimir Rovenski
• Języki publikacji: EN

Abstrakty

EN

We obtain a series of new integral formulae for a distribution of arbitrary codimension (and its orthogonal complement) given on a closed Riemannian manifold, which start from the formula by Walczak (1990) and generalize ones for foliations by several authors. For foliations on space forms our formulae reduce to the classical type formulae by Brito-Langevin-Rosenberg (1981) and Brito-Naveira (2000). The integral formulae involve the conullity tensor of a distribution, and certain components of the curvature tensor. The formulae also deal with a set of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For a special choice of the functions our formulae involve the Newton transformations of the co-nullity tensor.

Słowa kluczowe

EN

Distribution; Foliation; Riemannian metric; Mean curvatures; Co-nullity tensor; Integral formula; Divergence; Newton transformations

Kategorie tematyczne

• 53C12: Foliations (differential geometric aspects)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 3
• Strony: 558-577

Daty

wydano

2011-06-01

online

2011-03-22

Twórcy

autor

Vladimir Rovenski

• University of Haifa

Bibliografia

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• [14] Rovenski V., Walczak P., Extrinsic geometric flows on foliated manifolds I, preprint available at http://arxiv.org/abs/1003.1607v2
• [15] Rovenski V., Walczak P.G., Integral formulae on foliated symmetric spaces, Math. Ann. (in press), DOI: 10.1007/s00208-011-0637-4
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Identyfikatory

DOI

10.2478/s11533-011-0026-y