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 k-nullity foliations in Finsler geometry
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
Foliation, k-nullity, Finsler manifolds, curvature operator
مجله Bulletin of the Iranian Mathematical Society
شناسه DOI
پژوهشگران بهروز بیدآباد (نفر اول) ، مهدی رفیعی راد (نفر دوم)

چکیده

Here, a Finsler manifold (M, F) is considered with corresponding curvature tensor, regarded as 2-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of M determined by the curvature are introduced and called knullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive and each maximal integral manifold is totally geodesic. Characterization of the k-nullity foliation is given, as well as some results concerning constancy of the flag curvature, and completeness of their integral manifolds, providing completeness of (M, F). The introduced k-nullity space is a natural extension of nullity space in Riemannian geometry, introduced by Chern and Kuiper and enlarged to Finsler setting by Akbar-Zadeh and contains it as a special case.