The curvature of a congruence relative to a vector field of a complex Finsler hypersurface (Q1059290)

Given a vector field \(\lambda(u)\) representing a congruence of curves in a complex Finsler space \(F^ c_ n(X)\) of complex dimension n, and a vector field \(v(u)\) on a hypersurface \(F^ c_{n-1}(u)\) of \(F^ c_ n(X)\), two kinds of curvatures of \(\lambda\) relative to v are introduced and investigated. These notions reduce in special cases to the curvatures, resp. normal curvatures due to \textit{N. Prakash} [Tensor, New Ser. 11, 51-56 (1961; Zbl 0097.374); Ph. D. Thesis, Delhi Univ. (1960)]. \textit{H. Rund} [Can. J. Math. 8, 487-503 (1956; Zbl 0074.172)] and \textit{R. N. Kaul} [Tensor, New Ser. 7, 110-116 (1957; Zbl 0078.351)]. A similar investigation is performed if \(\lambda(u)\) and \(v(u)\) are replaced by \(\lambda(u,\dot u)\) and \(v(u,\dot u)\). This leads to similar statements concerning secondary curvatures.