ترغب بنشر مسار تعليمي؟ اضغط هنا

Conformal Vector Fields On Projectively Flat $(alpha,beta)$-Finsler Spaces

168   0   0.0 ( 0 )
 نشر من قبل Guojun Yang
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English
 تأليف Guojun Yang




اسأل ChatGPT حول البحث

In this paper, it is proved that any conformal vector field is homothetic on a locally projectively flat $(alpha,beta)$-space of non-Randers type in dimension $nge 3$, and the local solutions of such a vector field are determined. While on a locally projectively flat Randers space, examples showthat the conformal vector fields are not necessarily homothetic.



قيم البحث

اقرأ أيضاً

71 - Guojun Yang 2018
In this paper, we characterize conformal vector fields of any (regular or singular) $(alpha,beta)$-space with some PDEs. Further, we show some properties of conformal vector fields of a class of singular $(alpha,beta)$-spaces satisfying certain geometric conditions.
200 - Guojun Yang 2016
In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(alpha,beta)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to st udy conformal vector fields of some classes of $(alpha,beta)$ spaces under certain curvature conditions. Besides, we construct a family of non-homothetic conformal vector fields on a family of locally projectively Randers spaces.
143 - Guojun Yang 2015
An $(alpha,beta)$-manifold $(M,F)$ is a Finsler manifold with the Finsler metric $F$ being defined by a Riemannian metric $alpha$ and $1$-form $beta$ on the manifold $M$. In this paper, we classify $n$-dimensional $(alpha,beta)$-manifolds (non-Rander s type) which are positively complete and locally projectively flat. We show that the non-trivial class is that $M$ is homeomorphic to the $n$-sphere $S^n$ and $(S^n,F)$ is projectively related to a standard spherical Riemannian manifold, and then we obtain some special geometric properties on the geodesics and scalar flag curvature of $F$ on $S^n$, especially when $F$ is a metric of general square type.
In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric $F=alpha^2/beta$ with constant curvature $K$ and $|beta|_{alpha}=1$ is projectively flat if and only if $F$ is locally Minkowskian.
In this paper, we use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on $S^3$ with ${rm Ric} = 2 F^2$, ${rm Ric}=0$ and ${rm Ric}=- 2 F^2$, respectively. This family of metrics provide an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not.
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