scholarly journals Null hypersurfaces in indefinite nearly Kaehlerian Finsler spaces

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Vector Fields ◽  
Finsler Space ◽  
Second Fundamental Form ◽  
Finsler Spaces ◽  
Space Forms ◽  
Null Hypersurfaces ◽  
Geometric Conditions ◽  
Cr Structure ◽  
Sectional Curvatures ◽  
New Inequalities

We study the geometry of null hypersurfaces, $M$, in indefinite nearly Kaehlerian Finsler space forms $\mathbb{F}^{2n}$. We prove new inequalities involving the point-wise vertical sectional curvatures of $\mathbb{F}^{2n}$, based on two special vector fields on an umbilic hypersurface. Such inequalities generalize some known results on null hypersurfaces of Kaehlerian space forms. Furthermore, under some geometric conditions, we show that the null hypersurface $(M, B)$, where $B$ is the local second fundamental form of $M$, is locally isometric to the null product $M_{D}\times M_{D'}$, where $M_{D}$ and $M_{D'}$ are the leaves of the distributions $D$ and $D'$ which constitutes the natural null-CR structure on $M$.

scholarly journals Killing Vector Fields in Generalized Conformalβ-Change of Finsler Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Mallikarjun Yallappa Kumbar ◽  
Narasimhamurthy Senajji Kampalappa ◽  
Thippeswamy Komalobiah Rajanna ◽  
Kavyashree Ambale Rajegowda
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Finsler Space ◽  
Killing Vector ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finsler Spaces ◽  
Killing Vector Fields ◽  
Necessary And Sufficient

We consider a Finsler space equipped with a Generalized Conformalβ-change of metric and study the Killing vector fields that correspond between the original Finsler space and the Finsler space equipped with Generalized Conformalβ-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with Generalized Conformalβ-change of metric.

scholarly journals On Einstein null hypersurfaces of $(LCS)_{n+2}$-space forms

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Ricci Tensor ◽  
Null Hypersurface ◽  
Space Forms ◽  
Null Hypersurfaces ◽  
Geometric Conditions ◽  
Null Curves ◽  
Products Of Spheres

We show that ascreen null hypersurfaces of an $(n+2)$-dimensional Lorentzian concircular structure $(LCS)_{n+2}$-manifold admits an induced Ricci tensor. We, therefore, prove, under some geometric conditions, that an Einstein ascreen null hypersurface is locally a product of null curves and products of spheres.

scholarly journals On S-curvature of a homogeneous Finsler space with square metric

2020 ◽  
Vol 17 (02) ◽  
pp. 2050019
Author(s):  
Gauree Shanker ◽  
Sarita Rani
Keyword(s):  
Explicit Formula ◽  
Vector Fields ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Finsler Spaces ◽  
Invariant Vector ◽  
Homogeneous Finsler Space ◽  
The Mean ◽  
Invariant Vector Fields

The study of curvature properties of homogeneous Finsler spaces with [Formula: see text]-metrics is one of the central problems in Riemann–Finsler geometry. In this paper, the existence of invariant vector fields on a homogeneous Finsler space with square metric is proved. Further, an explicit formula for [Formula: see text]-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of [Formula: see text]-curvature, the mean Berwald curvature of aforesaid [Formula: see text]-metric is calculated.

scholarly journals KILLING FRAMES AND S-CURVATURE OF HOMOGENEOUS FINSLER SPACES

2014 ◽  
Vol 57 (2) ◽  
pp. 457-464 ◽  
Author(s):  
MING XU ◽  
SHAOQIANG DENG
Keyword(s):  
Explicit Formula ◽  
Vector Fields ◽  
Finsler Space ◽  
Killing Vector ◽  
Finsler Spaces ◽  
Killing Vector Fields ◽  
Randers Space ◽  
Homogeneous Finsler Space ◽  
Special Case

AbstractIn this paper, we first deduce a formula of S-curvature of homogeneous Finsler spaces in terms of Killing vector fields. Then we prove that a homogeneous Finsler space has isotropic S-curvature if and only if it has vanishing S-curvature. In the special case that the homogeneous Finsler space is a Randers space, we give an explicit formula which coincides with the previous formula obtained by the second author using other methods.

scholarly journals ON $S$-CURVATURE OF A HOMOGENEOUS FINSLER SPACE WITH RANDERS CHANGED SQUARE METRIC

2020 ◽  
pp. 673
Author(s):  
Sarita Rani ◽  
Gauree Shanker
Keyword(s):  
Explicit Formula ◽  
Vector Fields ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Finsler Spaces ◽  
Invariant Vector ◽  
Homogeneous Finsler Space ◽  
The Mean ◽  
Alpha Beta ◽  
Invariant Vector Fields

The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In the present paper, the existence of invariant vector fields on a homogeneous Finsler space with Randers changed square metric has been proved. Further, an explicit formula for $S$-curvature of Randers changed square metric has been established. Finally, using the formula of $S$-curvature, the mean Berwald curvature of afore said $(\alpha, \beta)$-metric has been calculated. 

ON THE GAUSS–BONNET FORMULA IN RIEMANN–FINSLER GEOMETRY

2002 ◽  
Vol 34 (3) ◽  
pp. 329-340 ◽  
Author(s):  
BRAD LACKEY
Keyword(s):  
Finsler Space ◽  
Finsler Geometry ◽  
Euler Class ◽  
Constant Volume ◽  
Finsler Spaces ◽  
Chern Connection ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Riemannian Case ◽  
Torsion Free

Using Chern's method of transgression, the Euler class of a compact orientable Riemann–Finsler space is represented by polynomials in the connection and curvature matrices of a torsion-free connection. When using the Chern connection (and hence the Christoffel–Levi–Civita connection in the Riemannian case), this result extends the Gauss–Bonnet formula of Bao and Chern to Finsler spaces whose indicatrices need not have constant volume.

Unitary vector fields are Fermi–Walker transported along Rytov–Legendre curves

2015 ◽  
Vol 12 (10) ◽  
pp. 1550111 ◽  
Author(s):  
Mircea Crasmareanu ◽  
Camelia Frigioiu
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Conformal Killing ◽  
Space Forms ◽  
Potential Vector ◽  
Legendre Curves ◽  
Complex Space Forms

Fix ξ a unitary vector field on a Riemannian manifold M and γ a non-geodesic Frenet curve on M satisfying the Rytov law of polarization optics. We prove in these conditions that γ is a Legendre curve for ξ if and only if the γ-Fermi–Walker covariant derivative of ξ vanishes. The cases when γ is circle or helix as well as ξ is (conformal) Killing vector filed or potential vector field of a Ricci soliton are analyzed and an example involving a three-dimensional warped metric is provided. We discuss also K-(para)contact, particularly (para)Sasakian, manifolds and hypersurfaces in complex space forms.

scholarly journals Analysis of Obata’s Differential Equations on Pointwise Semislant Warped Product Submanifolds of Complex Space Forms via Ricci Curvature

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Amira A. Ishan
Keyword(s):  
Differential Equations ◽  
Ricci Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Space Forms ◽  
Geometric Conditions ◽  
Isometric To A Sphere ◽  
Complex Space Forms

The present paper studies the applications of Obata’s differential equations on the Ricci curvature of the pointwise semislant warped product submanifolds. More precisely, by analyzing Obata’s differential equations on pointwise semislant warped product submanifolds, we demonstrate that, under certain conditions, the base of these submanifolds is isometric to a sphere. We also look at the effects of certain differential equations on pointwise semislant warped product submanifolds and show that the base is isometric to a special type of warped product under some geometric conditions.

Sign in / Sign up

Export Citation Format

Share Document