Geometry of Pseudo-Finsler Submanifolds

Bejancu, Aurel; Farran, Hani Reda

doi:10.1007/978-94-015-9417-2

Cited by 73 publications

(115 citation statements)

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“…C * ∇ is the the Levi-Civita connection of F κ and τ are respectively the curvature and the torsion of C (Bejancu and Farran, 2000).…”

Section: Methodsmentioning

confidence: 99%

“…Finsler geometry as in differential geometry plays an important role in other branches of science such as physics, biology, computer science and engineering. (Bejancu and Farran, 2000;Solange and Portugal, 2001;Brandt, 2005;Yılmaz and Bektaş, 2011) In this study, we examine inelastic flows of curves defined on the 3-dimensional Finsler manifolds . 3 …”

Section: Introductionmentioning

confidence: 99%

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Characterizations of Curves According to Elasticity in Finsler Manifold

Öǧrenmiş¹

2016

jist

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Physically, inelastic curve flow is qualified by the nonexistence of any strain energy taken from the motion. We have found out the changing equations for an inelastic curve whose length is preserved over all time.In this study, we give some characterizations for curves in terms of elasticity. Keywords:Finsler manifold, flow of a curve, frenet equations ÖZET: Fiziksel olarak, elastik olmayan bir eğri akışı, hareket kaynaklı bir enerji geriliminin bulunmaması olarak karakterize edilir. Biz bir elastik olmayan düzlem eğrisinin, yani yay uzunluğu her zaman korunan bir eğri için değişim denklemlerini ortaya çıkardık. Bu çalışmada, elastiklik açısından eğrilerin bazı karakterizasyonları verildi.

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“…C * ∇ is the the Levi-Civita connection of F κ and τ are respectively the curvature and the torsion of C (Bejancu and Farran, 2000).…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characterizations of Curves According to Elasticity in Finsler Manifold

Öǧrenmiş¹

2016

jist

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“…We shall borrow the method developed in real Finsler manifolds in [4]. This method is proved to be effective in complex Finsler holomorphic vector bundles.…”

Section: Gauss Codazzi and Ricci Equationsmentioning

confidence: 98%

Holomorphic curvature of complex Finsler submanifolds

Zhong

2009

Sci. China Math.

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Let M be a complex n-dimensional manifold endowed with a strongly pseudoconvex complex Finsler metric F . Let M be a complex m-dimensional submanifold of M , which is endowed with the induced complex Finsler metric F . Let D be the complex Rund connection associated with (M, F ). We prove that (a) the holomorphic curvature of the induced complex linear connection ∇ on (M, F ) and the holomorphic curvature of the intrinsic complex Rund connection ∇ * on (M, F ) coincide; (b) the holomorphic curvature of ∇ * does not exceed the holomorphic curvature of D; (c) (M, F ) is totally geodesic in (M, F ) if and only if a suitable contraction of the second fundamental form B(·, ·) of (M, F ) vanishes, i.e., B(χ, ι) = 0. Our proofs are mainly based on the Gauss, Codazzi and Ricci equations for (M, F ).

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“…Many geometers dedicated their attention to the study of relationships between the geometric properties of a Riemannian or a Finsler manifold M and those of its unit tangent sphere bundle, named also indicatrix ( [3,4,5,7,10,14], etc.). This research field, extended to the complex Finsler spaces, is very interesting and important, mainly because the complex indicatrix is a compact and strictly convex set surrounding the origin, used in the study of the volume of Finsler manifolds or in the study of the Laplacian or Hodge theories.…”

Section: Introductionmentioning

confidence: 99%

Classification of contact structures associated with the CR-structure of the complex indicatrix

Popovici

2017

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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By regarding the complex indicatrix as an embedded CR-hypersurface of the holomorphic tangent bundle in a fixed point, we analyze some aspects of the relations between its CR structure and the considered contact structure. Moreover, using the classification of the almost contact metric structures associated with a strongly pseudo-convex CRstructure, of D. Chinea and C. Gonzales, we determine the classes corresponding to the natural contact structure of the complex indicatrix and the new structures obtained under a gauge transformation.

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Geometry of Pseudo-Finsler Submanifolds

Cited by 73 publications

References 0 publications

Characterizations of Curves According to Elasticity in Finsler Manifold

Characterizations of Curves According to Elasticity in Finsler Manifold

Holomorphic curvature of complex Finsler submanifolds

Classification of contact structures associated with the CR-structure of the complex indicatrix

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