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1
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Paraquaternionic CR-submanifolds of paraquaternionic Kähler manifolds and semi-Riemannian submersions

100%
Ianuş S., Marchiafava S., Vîlcu G.
Open Mathematics
|
2010
|
tom 8
|
nr 4
735-753
EN
In this paper we introduce paraquaternionic CR-submanifolds of almost paraquaternionic hermitian manifolds and state some basic results on their differential geometry. We also study a class of semi-Riemannian submersions from paraquaternionic CR-submanifolds of paraquaternionic Kähler manifolds.
2
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Total curvature and volume of foliations on the sphere S 2

88%
Fawaz A.
Open Mathematics
|
2009
|
tom 7
|
nr 4
660-669
EN
In this paper we study a curvature integral associated with a pair of orthogonal foliations on the Riemann sphere S 2 and we compute the minimal value of the volume of meromorphic foliations.
3
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The automorphism groups of foliations with transverse linear connection

88%
Zhukova N., Dolgonosova A.
Open Mathematics
|
2013
|
tom 11
|
nr 12
2076-2088
EN
The category of foliations is considered. In this category morphisms are differentiable maps sending leaves of one foliation into leaves of the other foliation. We prove that the automorphism group of a foliation with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. This result extends the corresponding result of Macias-Virgós and Sanmartín Carbón for Riemannian foliations. In particular, our result is valid for Lorentzian and pseudo-Riemannian foliations.
4
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An invariant of nonpositively curved contact manifolds

75%
Kuessner T.
Open Mathematics
|
2011
|
tom 9
|
nr 1
173-183
EN
We define an invariant of contact structures and foliations (on Riemannian manifolds of nonpositive sectional curvature) which is upper semi-continuous with respect to deformations and thus gives an obstruction to the topology of foliations which can be approximated by isotopies of a given contact structure.
5
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Integral formulae for a Riemannian manifold with two orthogonal distributions

63%
Rovenski V.
Open Mathematics
|
2011
|
tom 9
|
nr 3
558-577
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.
6
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Deforming metrics of foliations

63%
Rovenski V., Wolak R.
Open Mathematics
|
2013
|
tom 11
|
nr 6
1039-1055
EN
Let M be a Riemannian manifold equipped with two complementary orthogonal distributions D and D ⊥. We introduce the conformal flow of the metric restricted to D with the speed proportional to the divergence of the mean curvature vector H, and study the question: When the metrics converge to one for which D enjoys a given geometric property, e.g., is harmonic, or totally geodesic? Our main observation is that this flow is equivalent to the heat flow of the 1-form dual to H, provided the initial 1-form is D ⊥-closed. Assuming that D ⊥ is integrable with compact and orientable leaves, we use known long-time existence results for the heat flow to show that our flow has a solution converging to a metric for which H = 0; actually, under some topological assumptions we can prescribe the mean curvature H.
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