# Integral formulae for a Riemannian manifold with two orthogonal distributions

Open Mathematics (2011)

- Volume: 9, Issue: 3, page 558-577
- ISSN: 2391-5455

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topVladimir Rovenski. "Integral formulae for a Riemannian manifold with two orthogonal distributions." Open Mathematics 9.3 (2011): 558-577. <http://eudml.org/doc/269769>.

@article{VladimirRovenski2011,

abstract = {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.},

author = {Vladimir Rovenski},

journal = {Open Mathematics},

keywords = {Distribution; Foliation; Riemannian metric; Mean curvatures; Co-nullity tensor; Integral formula; Divergence; Newton transformations; distribution; foliation; mean curvatures; co-nullity tensor; integral formula; divergence},

language = {eng},

number = {3},

pages = {558-577},

title = {Integral formulae for a Riemannian manifold with two orthogonal distributions},

url = {http://eudml.org/doc/269769},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Vladimir Rovenski

TI - Integral formulae for a Riemannian manifold with two orthogonal distributions

JO - Open Mathematics

PY - 2011

VL - 9

IS - 3

SP - 558

EP - 577

AB - 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.

LA - eng

KW - Distribution; Foliation; Riemannian metric; Mean curvatures; Co-nullity tensor; Integral formula; Divergence; Newton transformations; distribution; foliation; mean curvatures; co-nullity tensor; integral formula; divergence

UR - http://eudml.org/doc/269769

ER -

## References

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