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pro vyhledávání: '"Wolak Robert A."'
A Riemannian metric on a closed manifold is said to be geometrically formal if the wedge product of any two harmonic forms is harmonic; equivalently, the interior product of any two harmonic forms is harmonic. Given a Riemannian foliation on a closed
Externí odkaz:
http://arxiv.org/abs/2405.10867
Autor:
Wolak Robert A.
Publikováno v:
Demonstratio Mathematica, Vol 50, Iss 1, Pp 72-82 (2017)
Recent renewed interest in Sasakian manifolds is due mainly to the fact that they can provide examples of generalized Einstein manifolds, manifolds which are of great interest in mathematical models of various aspects of physical phenomena. Sasakian
Externí odkaz:
https://doaj.org/article/d70359abcbaa484ba8e217fdd3ae8f4c
The Hard Lefschetz Property (HLP) has recently been formulated in the context of isometric flows without singularities on manifolds. In this category, two versions of the HLP (transverse and not) have been proven to be equivalent, thus generalizing w
Externí odkaz:
http://arxiv.org/abs/2310.00466
Autor:
Mohseni, Rouzbeh, Wolak, Robert A.
Starting with a concise review of quaternionic geometry and quaternion K{\"a}hler manifolds, we define a transversely quaternion K{\"a}hler foliation. Then we formulate and prove the foliated versions of the now classical results of V.Y. Kraines and
Externí odkaz:
http://arxiv.org/abs/2202.02733
The Hard Lefschetz Property (HLP) is an important property which has been studied in several categories of the symplectic world. For Sasakian manifolds, this duality is satisfied by the basic cohomology (so, it is a transverse property), but a new ve
Externí odkaz:
http://arxiv.org/abs/2103.07441
Autor:
Rovenski, Vladimir, Wolak, Robert
We study the properties of Ricci curvature of ${\mathfrak{g}}$-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci curvature of the manifold and the Ricci curvature of the transverse ma
Externí odkaz:
http://arxiv.org/abs/2011.00799
Autor:
Mohseni, Rouzbeh, Wolak, Robert A.
The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate and prove
Externí odkaz:
http://arxiv.org/abs/2009.10491
Autor:
Rovenski, Vladimir, Wolak, Robert
In the paper we introduce new metric structures on $\mathfrak{g}$-foliations that are less rigid than the well-known structures: almost contact and 3-quasi-Sasakian structures as well as $f$-structures with parallelizable kernel and almost para-$\phi
Externí odkaz:
http://arxiv.org/abs/1905.07704
Autor:
Rovenski, Vladimir, Wolak, Robert
Publikováno v:
In Indagationes Mathematicae May 2022 33(3):518-532
Publikováno v:
Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales. Serie A. Matem\'aticas, (2019) 113(4), 4263-4286
For a Riemannian foliation F on a compact manifold M , J. A. \'Alvarez L\'opez proved that the geometrical tautness of F , that is, the existence of a Riemannian metric making all the leaves minimal submanifolds of M, can be characterized by the vani
Externí odkaz:
http://arxiv.org/abs/1702.06631