Regular Blaschke Quasi-umbilical Submanifolds in the Conformal Space ?_s~n

摘要

In [Nie, C. X. and Wu, C. X., Regular submanifolds in the conformal space ?_p~n, Chin. Ann. Math. Ser. B, 2012, vol. 33,no.5,pp. 695-714], the authors studied the regular submanifolds in the conformal space ?_s~n and introduced the submanifold theory in the conformalspace ?_s~n. This paper classifies the Blaschke quasi-umbilical submanifolds in the conformal space ?_s~n. It is proved that regular submanifolds in pseudo-Riemann space forms with constant scalar curvature and parallel mean curvature vector field are Blaschke quasi-umbilical submanifolds in the conformal space, and that any Blaschke quasi-umbilical submanifold in the conformal space is conformal equivalent to a regular submanifold with constant scalar curvature and parallel mean curvature vector field in pseudo-Riemann space forms. These results may be regarded as an extension of the classification of the conformal isotropic submanifolds in the conformal space ?_s~n.