On the volume of the projectivized tangent bundle in a complex Finsler manifold

2006 ◽  
Vol 86 (5) ◽  
pp. 458-463 ◽  
Author(s):  
Rongmu Yan
Keyword(s):  
Tangent Bundle ◽  
Finsler Manifold ◽  
Complex Finsler Manifold

Laplacians for the holomorphic tangent bundles with g-nature metrics on complex Finsler manifolds

2017 ◽  
Vol 28 (09) ◽  
pp. 1740011
Author(s):  
Hongjun Li ◽  
Chunhui Qiu ◽  
Weixia Zhu
Keyword(s):  
Laplace Operator ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Killing Vector ◽  
Finsler Manifold ◽  
Killing Vector Fields ◽  
Finsler Manifolds ◽  
Complex Finsler Manifold ◽  
Precise Relationship ◽  
Tangent Bundles

Let [Formula: see text] be a strongly pseudoconvex compact complex Finsler manifold. We first introduce a class of [Formula: see text]-nature metric [Formula: see text] for the slit holomorphic tangent bundle [Formula: see text] on [Formula: see text]. Then, we define the complex horizontal Laplacian [Formula: see text], and complex vertical Laplacian [Formula: see text], and obtain a precise relationship among [Formula: see text], [Formula: see text] and the Hodge–Laplace operator [Formula: see text] on [Formula: see text]. As an application, we discuss the holomorphic Killing vector fields associated to [Formula: see text].

HORIZONTAL LAPLACIAN ON TANGENT BUNDLE OF FINSLER MANIFOLD WITH g-NATURAL METRIC

2012 ◽  
Vol 09 (07) ◽  
pp. 1250061 ◽  
Author(s):  
ESMAEIL PEYGHAN ◽  
AKBAR TAYEBI ◽  
CHUNPING ZHONG
Keyword(s):  
Tangent Bundle ◽  
Vector Fields ◽  
Vector Bundles ◽  
Killing Vector ◽  
Finsler Manifold ◽  
Order Differential Operator ◽  
Finsler Manifolds ◽  
Scalar And Vector Fields ◽  
Matsumoto Metric ◽  
Weitzenböck Formula

Recently the third author studied horizontal Laplacians in real Finsler vector bundles and complex Finsler manifolds. In this paper, we introduce a class of g-natural metrics Ga,b on the tangent bundle of a Finsler manifold (M, F) which generalizes the associated Sasaki–Matsumoto metric and Miron metric. We obtain the Weitzenböck formula of the horizontal Laplacian associated to Ga,b, which is a second-order differential operator for general forms on tangent bundle. Using the horizontal Laplacian associated to Ga,b, we give some characterizations of certain objects which are geometric interest (e.g. scalar and vector fields which are horizontal covariant constant) on the tangent bundle. Furthermore, Killing vector fields associated to Ga,b are investigated.

scholarly journals On the vertical bundle of a pseudo-Finsler manifold

1999 ◽  
Vol 22 (3) ◽  
pp. 637-642 ◽  
Author(s):  
Aurel Bejancu ◽  
Hani Reda Farran
Keyword(s):  
Vertical Distribution ◽  
Tangent Bundle ◽  
Finsler Manifold ◽  
Geometric Properties ◽  
Liouville Distribution ◽  
The Vertical Distribution

We define the Liouville distribution on the tangent bundle of a pseudo-Finsler manifold and prove that it is integrable. Also, we find geometric properties of both leaves of Liouville distribution and the vertical distribution.

scholarly journals Infinitesimal Hilbertianity of Weighted Riemannian Manifolds

2019 ◽  
Vol 63 (1) ◽  
pp. 118-140 ◽  
Author(s):  
Danka Lučić ◽  
Enrico Pasqualetto
Keyword(s):  
Hilbert Space ◽  
Riemannian Manifold ◽  
Sobolev Space ◽  
Riemannian Manifolds ◽  
Tangent Bundle ◽  
Radon Measure ◽  
Finsler Manifold ◽  
Carnot Groups

AbstractThe main result of this paper is the following: anyweightedRiemannian manifold$(M,g,\unicode[STIX]{x1D707})$,i.e., a Riemannian manifold$(M,g)$endowed with a generic non-negative Radon measure$\unicode[STIX]{x1D707}$, isinfinitesimally Hilbertian, which means that its associated Sobolev space$W^{1,2}(M,g,\unicode[STIX]{x1D707})$is a Hilbert space.We actually prove a stronger result: the abstract tangent module (à la Gigli) associated with any weighted reversible Finsler manifold$(M,F,\unicode[STIX]{x1D707})$can be isometrically embedded into the space of all measurable sections of the tangent bundle of$M$that are$2$-integrable with respect to$\unicode[STIX]{x1D707}$.By following the same approach, we also prove that all weighted (sub-Riemannian) Carnot groups are infinitesimally Hilbertian.

A framed f-structure on the tangent bundle of a Finsler manifold

2012 ◽  
Vol 104 (1) ◽  
pp. 23-41 ◽  
Author(s):  
Esmaeil Peyghan ◽  
Chunping Zhong
Keyword(s):  
Tangent Bundle ◽  
Finsler Manifold
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