17 بهمن 1401
مهدي رفيعي راد

مهدی رفیعی راد

مرتبه علمی: دانشیار
نشانی:
تحصیلات: دکترای تخصصی / ریاضی محض-هندسه
تلفن: 01135302464
دانشکده: دانشکده علوم ریاضی

مشخصات پژوهش

عنوان ON THE RIEMANN CURVATURE OPERATORS IN RANDERS SPACES
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
Riemann curvature operator; Randers metric; principal curvature; S-curvature
مجله INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
شناسه DOI 10.1142/S0219887813500448
پژوهشگران مهدی رفیعی راد (نفر اول)

چکیده

The Riemann curvature in Riemann–Finsler geometry can be regarded as a collection of linear operators on the tangent spaces. The algebraic properties of these operators may be linked to the geometry and the topology of the underlying space. The principal curvatures of a Finsler space (M,F) at a point x are the eigenvalues of the Riemann curvature operator at x. They are real functions κ on the slit tangent manifold TM0. A principal curvature κ(x, y) is said to be isotropic respectively, quadratic) if κ(x, y)/F (x, y) is a function of x only (respectively, κ(x, y) is quadratic with respect to y). On the other hand, the Randers metrics are the most popular and prominent metrics in pure and applied disciplines. Here, it is proved that if a Randers metric admits an isotropic principal curvature, then F is of isotropic S-curvature. The same result is also established for F to admit a quadratic principal curvature. These results extend Shen’s verbal results about Randers metrics of scalar flag curvature K = K(x) as well as those Randers metrics with quadratic Riemann curvature operator. The Riemann curvature Ri k may be broken into two operators Ri k and J i k. The isotropic and quadratic principal curvature are characterized in terms of the eigenvalues of R and J .