Conharmonic Tensor of Certain Classes of Almost Hermitian Manifold

2010 ◽  
Author(s):  
Habeeb Mtashar Abood ◽  
Gassan Irhaim Lafta
Keyword(s):  
Hermitian Manifold ◽  
Almost Hermitian Manifold

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

On nonexistence of Kenmotsu structure on аст-hypersurfaces of cosymplectic type of a Kählerian manifold

2019 ◽  
pp. 23-28
Author(s):  
G. Banaru
Keyword(s):  
Hermitian Manifold ◽  
Structural Equations ◽  
Type I ◽  
Almost Hermitian Manifold ◽  
Almost Contact Metric Structure ◽  
Almost Contact Metric ◽  
Contact Metric Structure ◽  
Metric Structures ◽  
Kählerian Manifold ◽  
Almost Contact Metric Structures

Almost contact metric (аст-)structures induced on oriented hypersurfaces of a Kählerian manifold are considered in the case when these аст- structures are of cosymplectic type, i. e. the contact form of these structures is closed. As it is known, the Kenmotsu structure is the most important non-trivial example of an almost contact metric structure of cosymplectic type. The Cartan structural equations of the almost contact metric structure of cosymplectic type on a hypersurface of a Kählerian manifold are obtained. It is proved that an almost contact metric structure of cosymplectic type on a hypersurface of a Kählerian manifold of dimension at least six cannot be a Kenmotsu structure. Moreover, it follows that oriented hypersurfaces of a Kählerian manifold of dimension at least six do not admit non-trivial almost contact metric structures of cosymplectic type that belong to any well studied class of аст-structures. The present results generalize some results on almost contact metric structures on hypersurfaces of an almost Hermitian manifold obtained earlier by V. F. Kirichenko, L. V. Stepanova, A. Abu-Saleem, M. B. Banaru and others.

scholarly journals Slant immersions

1990 ◽  
Vol 41 (1) ◽  
pp. 135-147 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Isometric Immersion ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Slant Immersion

A slant immersion is defined as an isometric immersion from a Riemannnian manifold into an almost Hermitian manifold with constant Wirtinger angle. In this article we give some fundamental results concerning slant immersions. Several results on slant surfaces in ℂ2 are also proved.

scholarly journals Four-Dimensional Almost Einstein Manifolds with Skew-Circulant Structres

2019 ◽  
Author(s):  
Iva Dokuzova ◽  
Dimitar Razpopov
Keyword(s):  
Tangent Space ◽  
Local Coordinate System ◽  
Complex Structure ◽  
Hermitian Manifold ◽  
Circulant Matrices ◽  
Fourth Power ◽  
Einstein Manifolds ◽  
Almost Hermitian Manifold ◽  
Riemannian Connection ◽  
Skew Circulant

We consider a four-dimensional Riemannian manifold M equipped with an additional tensor structure S, whose fourth power is minus identity and the second power is an almost complex structure. In a local coordinate system the components of the metric g and the structure S form skew-circulant matrices. Both structures S and g are compatible, such that an isometry is induced in every tangent space of M. By a special identity for the curvature tensor, generated by the Riemannian connection of g, we determine classes of an Einstein manifolds and an almost Einstein manifolds. For such manifolds we obtain propositions for the sectional curvatures of some special 2-planes in a tangent space of M. We consider an almost Hermitian manifold associated with the studied manifold and find conditions for g, under which it is a Kähler manifold. We construct some examples of the considered manifolds on Lie groups.

scholarly journals Compact Hermitian surfaces of pointwise constant holomorphic sectional curvature

1995 ◽  
Vol 37 (3) ◽  
pp. 343-349 ◽  
Author(s):  
Kouei Sekigawa ◽  
Takashi Koda
Keyword(s):  
Sectional Curvature ◽  
Differentiable Function ◽  
Tangent Bundle ◽  
Complex Structure ◽  
Hermitian Manifold ◽  
Holomorphic Sectional Curvature ◽  
Almost Complex Structure ◽  
Almost Hermitian Manifold ◽  
Almost Complex ◽  
Unit Tangent Bundle

Let M = (M, J, g) be an almost Hermitian manifold and U(M)the unit tangent bundle of M. Then the holomorphic sectional curvature H = H(x) can be regarded as a differentiable function on U(M). If the function H is constant along each fibre, then M is called a space of pointwise constant holomorphic sectional curvature. Especially, if H is constant on the whole U(M), then M is called a space of constant holomorphic sectional curvature. An almost Hermitian manifold with an integrable almost complex structure is called a Hermitian manifold. A real 4-dimensional Hermitian manifold is called a Hermitian surface. Hermitian surfaces of pointwise constant holomorphic sectional curvature have been studied by several authors (cf. [2], [3], [5], [6] and so on).

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