Iranian Journal of Mathematical Sciences and Informatics, 2016
We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula ... more We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula holds for double coset Lie hypergroups and show that certain representations of the Lie group lift to representations of the double coset Lie hypergroup. We characterize smooth (analytic) vectors of these lifted representations.
journal of sciences islamic republic of iran, 2016
Providing an appropriate definition of a horizontal subbundle of a Lie algebroid will lead to con... more Providing an appropriate definition of a horizontal subbundle of a Lie algebroid will lead to construction of a better framework on Lie algebriods. In this paper, we give a new and natural definition of a horizontal subbundle using the prolongation of a Lie algebroid and then we show that any linear connection on a Lie algebroid generates a horizontal subbundle and vice versa. The same correspondence will be proved for any covariant derivative on a Lie algebroid.
In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition... more In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by means of the induced Poisson structures on the integral submanifolds. Moreover, for any compatible triple with invariant metric and admissible almost complex structure, we show that the bracket annihilates on the kernel of the anchor map.
In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition... more In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by means of the induced Poisson structures on the integral submanifolds. Moreover, for any compatible triple with invariant metric and admissible almost complex structure, we show that the bracket annihilates on the kernel of the anchor map.
Iranian Journal of Mathematical Sciences and Informatics, 2011
The Lie derivation of multivector fields along multivector fields has been introduced by Schouten... more The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see (10, 11)), and studdied for example in (5) and (12). In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this con- cept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and other familiar concepts. Also in spinor bundles, we introduce a covariant derivation along multivector fields and call it the Clifford covariant derivation of that spinor bundle, which is related to its structure and has a natural relation to its Dirac operator.
In this paper, we study a class of Finsler metrics which contains the class of P-reducible metric... more In this paper, we study a class of Finsler metrics which contains the class of P-reducible metrics. Finsler metrics in this class are called generalized P-reducible metrics. We consider generalized P-reducible metrics with scalar flag curvature and find a condition under which these metrics reduce to C-reducible metrics. This generalize Matsumoto's theorem, which describes the equivalency of C-reducibility and P-reducibility on Finsler manifolds with scalar curvature. Then we show that generalized P-reducible metrics with vanishing stretch curvature are C-reducible.
In this article we study isometric immersions of nearly Kähler manifolds into a space form (speci... more In this article we study isometric immersions of nearly Kähler manifolds into a space form (specially Euclidean space) and show that every nearly Kähler submanifold of a space form has an umbilic foliation whose leafs are 6-dimensional nearly Kähler manifolds. Moreover using this foliation we show that there is no non-homogeneous 6-dimensional nearly Kähler submanifold of a space form. We prove some results towards a classification of nearly Kähler hypersurfaces in standard space forms.
We study the foliation space of complex and invariant (by torsion of intrinsic Hermitian connecti... more We study the foliation space of complex and invariant (by torsion of intrinsic Hermitian connection) umbilic distribution on an isometric immersion from a nearly K\"ahler manifold $M$ into the Euclidean space. Under suitable conditions this leaf space is nearly K\"ahler and $M$ can be decomposed into a product of this leaf space and a 6-dimensional locally homogeneous nearly K\"ahler manifold.
Noting that the complete lift of a Rimannian metric defined on a differentiable manifold is not 0... more Noting that the complete lift of a Rimannian metric defined on a differentiable manifold is not 0-homogeneous on the fibers of the tangent bundle . In this paper we introduce a new lift which is 0-homogeneous. It determines on slit tangent bundle a pseudo-Riemannian metric, which depends only on the metric . We study some of the geometrical properties of this pseudo-Riemannian space and define the natural almost complex structure and natural almost product structure which preserve the property of homogeneity and find some new results.
Abstract The complete lift of a Riemannian metric g on a differentiable manifold M is not 0-homog... more Abstract The complete lift of a Riemannian metric g on a differentiable manifold M is not 0-homogeneous on the fibers of the tangent bundle TM. In this paper we introduce a new kind of lift G of g, which is 0-homogeneous. It determines a pseudo-Riemannian metric on TM, ...
Journal of Mathematical Analysis and Applications, 2008
Let M be an n-dimensional Riemannian manifold and TM its tangent bundle. The conformal and fiber ... more Let M be an n-dimensional Riemannian manifold and TM its tangent bundle. The conformal and fiber preserving vector fields on TM have well-known physical interpretations and have been studied by physicists and geometers using some Riemannian and pseudo-Riemannian lift metrics on TM. Here we consider the Riemannian or pseudo-Riemannian lift metric G on TM which is in some senses more general than other lift metrics previously defined on TM, and seems to complete these works. Next we study the lift conformal vector fields on (TM, G).
In this paper the symmetric differential and symmetric Lie deriv- ative are introduced. Using the... more In this paper the symmetric differential and symmetric Lie deriv- ative are introduced. Using these tools derivations of the algebra of symmetric tensors are classified. We also define a Frolicher-Nijenhuis bracket for vector valued symmetric tensors.
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Papers by Abbas Heydari