On Concircularly Recurrent Finsler Manifolds

Abstract

Two special Finsler spaces have been introduced and investigated, namely $R^h$-recurrent Finsler space and consircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: 1. A concircularly flat Finsler manifold is necessarily of constant curvature (Theorem A); 2. Every $R^h$-recurrent Finsler manifold is concirculaly recurrent with the same recurrence form (Theorem B); 3. Every horizontally integrable concircularly recurrent Finsler manifold is $R^h$-recurrent with the same recurrence form (Theorem C). The whole work is formulated in a coordinate-free form.

LaTex file, 13 pages. arXiv admin note: text overlap with arXiv:1201.2012

References in corpus (1)

• Geometric objects associated with the fundamental connections in Finsler geometry

Cited by in corpus (4)

• Concircular curvature on warped product manifolds and applications
• Some Types of Recurrence in Finsler geometry
• New Special Finsler Spaces
• On Hyper-Generalized Recurrent Finsler Spaces