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On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor

Hiroshi Endo (1991)

Colloquium Mathematicae

For Sasakian manifolds, Matsumoto and Chūman [6] defined the contact Bochner curvature tensor (see also Yano [9]). Hasegawa and Nakane [4] and Ikawa and Kon [5] have studied Sasakian manifolds with vanishing contact Bochner curvature tensor. Such manifolds were studied in the theory of submanifolds by Yano ([9] and [10]). In this paper we define an extended contact Bochner curvature tensor in K-contact Riemannian manifolds and call it the E-contact Bochner curvature tensor. Then we show that a K-contact...

On left invariant CR structures on SU ( 2 )

Andreas Čap (2006)

Archivum Mathematicum

There is a well known one–parameter family of left invariant CR structures on S U ( 2 ) ≅ S 3 . We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.

On Levi-flat hypersurfaces tangent to holomorphic webs

Arturo Fernández-Pérez (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We investigate real analytic Levi-flat hypersurfaces tangent to holomorphic webs. We introduce the notion of first integrals for local webs. In particular, we prove that a k -web with finitely many invariant subvarieties through the origin tangent to a Levi-flat hypersurface has a holomorphic first integral.

On Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures

Josef Janyška (2016)

Archivum Mathematicum

We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the structure of a Lie algebra. We describe Lie subalgebras in this Lie algebra given by pairs generating infinitesimal symmetries of basic tensor fields given by the almost-cosymplectic-contact structure.

On Lie algebras of vector fields related to Riemannian foliations

Tomasz Rybicki (1993)

Annales Polonici Mathematici

Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.

On Liouville forms

Paulette Libermann (2000)

Banach Center Publications

We give different notions of Liouville forms, generalized Liouville forms and vertical Liouville forms with respect to a locally trivial fibration π:E → M. These notions are linked with those of semi-basic forms and vertical forms. We study the infinitesimal automorphisms of these forms; we also investigate the relations with momentum maps.

On local flatness of manifolds with AHS-structures

Čap, Andreas, Slovák, Jan (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

Summary: The AHS-structures on manifolds are the simplest cases of the so called parabolic geometries which are modeled on homogeneous spaces corresponding to a parabolic subgroup in a semisimple Lie group. It covers the cases where the negative parts of the graded Lie algebras in question are abelian. In the series the authors developed a consistent frame bundle approach to the subject. Here we give explicit descriptions of the obstructions against the flatness of such structures based on the latter...

On local isometric immersions into complex and quaternionic projective spaces

Hans Jakob Rivertz (2011)

Archivum Mathematicum

We will prove that if an open subset of ℂ P n is isometrically immersed into ℂ P m , with m < ( 4 / 3 ) n - 2 / 3 , then the image is totally geodesic. We will also prove that if an open subset of ℍ P n isometrically immersed into ℍ P m , with m < ( 4 / 3 ) n - 5 / 6 , then the image is totally geodesic.

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