RULED SUBMANIFOLDS OF FINITE TYPE IN LORENTZIAN SPACE-TIMES Kim, Dong-Soo;
In this article, we study ruled submanifolds with nonde-generate rulings in a Lorentzian space-time, which have finite type immersion. We give a condition for k-finite type submanifolds to be of finite type.
ruled submanifold;finite type submanifold;minimal submanifold;
B.-Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22(1996), 117-317.
B.-Y. Chen, Total mean curvature and submanifolds of finite type, World Scientific Publ. (1984).
B.-Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken, Ruled surfaces of finite type, Bull. Austral. Math. Soc. 42 (1990), 447-453.
F. Dillen, I. Van de Woestijne, L. Verstraelen and J. Walrave, Ruled surfaces of finite type in Minkowski spaces, Results Math. 27(1995), 250-255.
D.-S. Kim, Ruled surfaces of finite type in Lorentzian space-times, Honam Math. J. 31(2009), 177-183.
D.-S. Kim and Y. H. Kim, B-scrolls with non-diagonalizable shape operators, Rocky Mount. J. Math. 33(2003), 175-190.
D.-S. Kim and Y. H. Kim, Finite type ruled hypersurfaces in Lorentz-Minkowski space, Honam Math. J. 30(2008), 743-748.
D.-S. Kim and Y. H. Kim, Classification of ruled submanifolds in a Lorentz-Minkowski space, Submitted.
D.-S. Kim, Y. H. Kim and D. W. Yoon, Characterization of generalized B-scrolls and cylinders over finite type curves, Indian J. Pure Appl. Math. 34 (2003), 1523-1532.
D.-S. Kim and Y. H. Kim and D. W. Yoon Finite type ruled surfaces in Lorentz-Minkowski space, Taiwanese J. Math. 11(2007), 1-13.