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Remarks on F-planar curves and their generalizations

Jaroslav Hrdina (2011)

Banach Center Publications

Generalized planar curves (A-curves) are more general analogues of F-planar curves and geodesics. In particular, several well known geometries are described by more than one affinor. The best known example is the almost quaternionic geometry. A new approach to this topic (A-structures) was started in our earlier papers. In this paper we expand the concept of A-structures to projective A-structures.

Remarks on local Lie algebras of pairs of functions

Josef Janyška (2018)

Czechoslovak Mathematical Journal

Starting by the famous paper by Kirillov, local Lie algebras of functions over smooth manifolds were studied very intensively by mathematicians and physicists. In the present paper we study local Lie algebras of pairs of functions which generate infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds.

Remarks on Special Symplectic Connections

Martin Panák, Vojtěch Žádník (2008)

Archivum Mathematicum

The notion of special symplectic connections is closely related to parabolic contact geometries due to the work of M. Cahen and L. Schwachhöfer. We remind their characterization and reinterpret the result in terms of generalized Weyl connections. The aim of this paper is to provide an alternative and more explicit construction of special symplectic connections of three types from the list. This is done by pulling back an ambient linear connection from the total space of a natural scale bundle over...

Ricci curvature of real hypersurfaces in complex hyperbolic space

Bang-Yen Chen (2002)

Archivum Mathematicum

First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.

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