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Autor:
Rafaela F. do Prado, Lino Grama
Publikováno v:
Complex Manifolds, Vol 5, Iss 1, Pp 122-132 (2018)
In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow.We provide examples where the stability (non-stability) is preserved under the Ricci flow and an example where the Ricci flow does not p
Autor:
Young Jin Suh, Eunmi Pak
Publikováno v:
Open Mathematics, Vol 12, Iss 12, Pp 1840-1851 (2014)
Regarding the generalized Tanaka-Webster connection, we considered a new notion of $$\mathfrak{D}^ \bot$$ -parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G 2(ℂ m+2) and proved that a real hypersurface
Autor:
Mikhael Gromov
Publikováno v:
Open Mathematics, Vol 12, Iss 7, Pp 923-951 (2014)
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instanc
Autor:
N. I. Zhukova, Anna Yu. Dolgonosova
Publikováno v:
Open Mathematics, Vol 11, Iss 12, Pp 2076-2088 (2013)
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
Autor:
Graham Hall
Publikováno v:
Open Mathematics, Vol 10, Iss 5, Pp 1763-1770 (2012)
This paper discusses the connection between projective relatedness and conformal flatness for 4-dimensional manifolds admitting a metric of signature (+,+,+,+) or (+,+,+,−). It is shown that if one of the manifolds is conformally flat and not of th
Autor:
Krishan L. Duggal
Publikováno v:
Open Mathematics, Vol 10, Iss 5, Pp 1789-1800 (2012)
This paper deals with a family of lightlike (null) hypersurfaces (Hu) of a Lorentzian manifold M such that each null normal vector l of Hu is not entirely in Hu, but, is defined in some open subset of M around Hu. Although the family (Hu) is not uniq
Publikováno v:
Open Mathematics, Vol 10, Iss 2, Pp 451-455 (2012)
Considering the notion of Jacobi type vector fields for a real hypersurface in a complex two-plane Grassmannian, we prove that if a structure vector field is of Jacobi type it is Killing. As a consequence we classify real hypersurfaces whose structur
Publikováno v:
Open Mathematics, Vol 9, Iss 3, Pp 578-582 (2011)
We prove the non-existence of real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type.
Autor:
Thilo Kuessner
Publikováno v:
Open Mathematics, Vol 9, Iss 1, Pp 173-183 (2011)
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
Autor:
Georges Habib, Nicolas Ginoux
Publikováno v:
Open Mathematics, Vol 8, Iss 5, Pp 950-965 (2010)
HAL
Central European Journal of Mathematics
Central European Journal of Mathematics, Springer Verlag, 2010, 8, pp.950-965
HAL
Central European Journal of Mathematics
Central European Journal of Mathematics, Springer Verlag, 2010, 8, pp.950-965
International audience; We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on Sasakian and on $3$-dimensional manifolds and partially classify