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Almost c-spinorial geometry

Roland Púček (2017)

Archivum Mathematicum

Almost c-spinorial geometry arises as an interesting example of the metrisability problem for parabolic geometries. It is a complex analogue of real spinorial geometry. In this paper, we first define the type of parabolic geometry in question, then we discuss its underlying geometry and its homogeneous model. We compute irreducible components of the harmonic curvature and discuss the conditions for regularity. In the second part of the paper, we describe the linearisation of the metrisability problem...

Almost Hermitian surfaces with vanishing Tricerri-Vanhecke Bochner curvature tensor

Y. Euh, J. Lee, J. H. Park, K. Sekigawa, A. Yamada (2011)

Colloquium Mathematicae

We study the curvature properties of almost Hermitian surfaces with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. Local structure theorems for such almost Hermitian surfaces are provided, and several examples related to these theorems are given.

Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact 3 -structure

Francisco Martín Cabrera (1998)

Czechoslovak Mathematical Journal

We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds which are not...

Almost invariant submanifolds for compact group actions

Alan Weinstein (2000)

Journal of the European Mathematical Society

We define a C 1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G , there is a G -invariant submanifold C 1 -close to N . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros of sections...

Almost symplectic structures and harmonic morphisms

Jean-Marie Burel (2004)

Bollettino dell'Unione Matematica Italiana

In this paper, we introduce the notion of symplectic harmonic maps between tamed manifolds and establish some properties. In the case where the manifolds are almost Hermitian manifolds, we obtain a new method to contruct harmonic maps with minimal fibres. We finally present examples of such applications between projectives spaces.

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