• 호남수학학술지
• /
• 제32권2호
• /
• pp.261-269
• /
• 2010

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.

• 대한수학회논문집
• /
• 제32권1호
• /
• pp.107-118
• /
• 2017

In this paper we study CR-submanifolds of maximal CR-dimension by investigating extrinsic behaviors of integral curves of characteristic vector field on them. Also we consider the notion of ruled CR-submanifold of maximal CR-dimension which is a generalization of that of ruled real hypersurface and find some characterizations of ruled CR-submanifold of maximal CR-dimension concerning extrinsic shapes of integral curves of the characteristic vector field and those of CR-Frenet curves.

• 대한수학회보
• /
• 제51권3호
• /
• pp.823-829
• /
• 2014

Ruled submanifolds in Euclidean space satisfying some algebraic equations concerning the Laplace operator related to the isometric immersion and Gauss map are studied. Cylinders over a finite type curve or generalized helicoids are characterized with such algebraic equations.

• 대한수학회지
• /
• 제53권6호
• /
• pp.1309-1330
• /
• 2016

As a generalizing certain geometric property occurred on the helicoid of 3-dimensional Euclidean space regarding the Gauss map, we study ruled submanifolds in a Euclidean space with pointwise 1-type Gauss map of the first kind. In this paper, as new examples of cylindrical ruled submanifolds in Euclidean space, we construct generalized circular cylinders and characterize such ruled submanifolds and minimal ruled submanifolds of Euclidean space with pointwise 1-type Gauss map of the first kind.