ترغب بنشر مسار تعليمي؟ اضغط هنا

Generalized P-Reducible $(alpha, beta)$-Metrics with Vanishing S-curvature

61   0   0.0 ( 0 )
 نشر من قبل Akbar Tayebi
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we study one of the open problems in Finsler geometry which presented by Matsumoto-Shimada about the existence of P-reducible metric which is not C-reducible. For this aim, we study a class of Finsler metrics called generalized P-reducible metrics that contains the class of P-reducible metrics. We prove that every generalized P-reducible $(alpha, beta)$-metric with vanishing S-curvature reduces to a Berwald metric or C-reducible metric. It results that there is not any concrete P-reducible $(alpha,beta)$-metric with vanishing S-curvature.



قيم البحث

اقرأ أيضاً

136 - Guojun Yang 2014
An $(alpha,beta)$-metric is defined by a Riemannian metric $alpha$ and $1$-form $beta$. In this paper, we study a known class of two-dimensional $(alpha,beta)$-metrics of vanishing S-curvature. We determine the local structure of those metrics and sh ow that those metrics are Einsteinian (equivalently, isotropic flag curvature) but generally are not Ricci-flat.
123 - Zhongmin Shen 2020
Every Riemannian metric or Finsler metric on a manifold induces a spray via its geodesics. In this paper, we discuss several expressions for the X-curvature of a spray. We show that the sprays obtained by a projective deformation using the S-curvatur e always have vanishing X-curvature. Then we establish the Beltrami Theorem for sprays with X=0
Motivated by the work of Li and Mantoulidis, we study singular metrics which are uniformly Euclidean $(L^infty)$ on a compact manifold $M^n$ ($nge 3$) with negative Yamabe invariant $sigma(M)$. It is well-known that if $g$ is a smooth metric on $M$ w ith unit volume and with scalar curvature $R(g)ge sigma(M)$, then $g$ is Einstein. We show, in all dimensions, the same is true for metrics with edge singularities with cone angles $leq 2pi$ along codimension-2 submanifolds. We also show in three dimension, if the Yamabe invariant of connected sum of two copies of $M$ attains its minimum, then the same is true for $L^infty$ metrics with isolated point singularities.
120 - Wu Zhou , Fangyang Zheng 2021
We examine the class of compact Hermitian manifolds with constant holomorphic sectional curvature. Such manifolds are conjectured to be Kahler (hence a complex space form) when the constant is non-zero and Chern flat (hence a quotient of a complex Li e group) when the constant is zero. The conjecture is known in complex dimension two but open in higher dimensions. In this paper, we establish a partial solution in complex dimension three by proving that any compact Hermitian threefold with zero real bisectional curvature must be Chern flat. Real bisectional curvature is a curvature notion introduced by Xiaokui Yang and the second named author in 2019, generalizing holomorphic sectional curvature. It is equivalent to the latter in the Kahler case and is slightly stronger in general.
164 - Guojun Yang 2013
An $(alpha,beta)$-metric is defined by a Riemannian metric and $1$-form. In this paper, we investigate the known characterization for $(alpha,beta)$-metrics of isotropic S-curvature. We show that such a characterization should hold in dimension $nge 3$, and for the 2-dimensional case, there is one more class of isotropic S-curvature than the higher dimensional ones. Further, we construct corresponding examples for every two-dimensional class, especially for the class that the norm of $beta$ with respect to $alpha$ is not a constant.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا