Coordinate finite-type submanifolds

1991 ◽  
Vol 37 (2) ◽  
Author(s):  
Thomas Hasanis ◽  
Theodore Vlachos
Keyword(s):  
Finite Type ◽  
Finite Type Submanifolds

scholarly journals The Chen-type of the noncompact cyclides of Dupin

1994 ◽  
Vol 36 (1) ◽  
pp. 71-75 ◽  
Author(s):  
Filip Defever ◽  
Ryszard Deszcz ◽  
Leopold Verstraelen
Keyword(s):  
Euclidean Space ◽  
Finite Type ◽  
Minimal Submanifolds ◽  
First Results ◽  
Finite Type Submanifolds ◽  
Submanifolds Of Finite Type

Minimal submanifolds of a Euclidean space are contained in a much larger class of submanifolds, namely in the class of submanifolds of finite type. Submanifolds of finite type were introduced about a decade ago by B. Y. Chen in [2]; the first results on this subject have been collected in the books [2], [3].

Finite type pseudo-umbilical submanifolds in a hypersphere

1991 ◽  
Vol 44 (3) ◽  
pp. 391-396
Author(s):  
Shi-Jie Li
Keyword(s):  
Finite Type ◽  
Finite Type Submanifolds

The notion of finite type submanifolds was introduced by B.Y. Chen. In this article we study 2- and 3-type pseudo-umbilical submanifolds in a hypersphere. Two theorems in this respect are obtained.

scholarly journals Some open problems and conjectures on submanifolds of finite type: recent development

2014 ◽  
Vol 45 (1) ◽  
pp. 87-108 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Finite Type ◽  
Detailed Account ◽  
Biharmonic Submanifolds ◽  
Open Problems ◽  
Detailed Survey ◽  
First Results ◽  
Finite Type Submanifolds ◽  
Submanifolds Of Finite Type

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type submanifolds was published in [40]. A detailed survey of the results, up to 1996, on this subject was given by the author in [48]. Recently, the study of finite type submanifolds, in particular, of biharmonic submanifolds, have received a growing attention with many progresses since the beginning of this century. In this article, we provide a detailed account of recent development on the problems and conjectures listed in [40].

ON FINITE TYPE 3-MANIFOLD INVARIANTS I

1996 ◽  
Vol 05 (04) ◽  
pp. 441-461 ◽  
Author(s):  
STAVROS GAROUFALIDIS
Keyword(s):  
Vector Space ◽  
Finite Type ◽  
Commutative Algebra ◽  
Integral Homology ◽  
Knot Invariants ◽  
Finite Type Invariants ◽  
Definition Of ◽  
Type 3

Recently Ohtsuki [Oh2], motivated by the notion of finite type knot invariants, introduced the notion of finite type invariants for oriented, integral homology 3-spheres. In the present paper we propose another definition of finite type invariants of integral homology 3-spheres and give equivalent reformulations of our notion. We show that our invariants form a filtered commutative algebra. We compare the two induced filtrations on the vector space on the set of integral homology 3-spheres. As an observation, we discover a new set of restrictions that finite type invariants in the sense of Ohtsuki satisfy and give a set of axioms that characterize the Casson invariant. Finally, we pose a set of questions relating the finite type 3-manifold invariants with the (Vassiliev) knot invariants.

Perturbations of multidimensional shifts of finite type

2010 ◽  
Vol 31 (2) ◽  
pp. 483-526 ◽  
Author(s):  
RONNIE PAVLOV
Keyword(s):  
Finite Type ◽  
Lower Bounds ◽  
Symbolic Dynamics ◽  
Upper And Lower Bounds ◽  
Shift Of Finite Type ◽  
Strongly Irreducible ◽  
Dimensional Cube

AbstractIn this paper, we study perturbations of multidimensional shifts of finite type. Specifically, for any ℤd shift of finite type X with d>1 and any finite pattern w in the language of X, we denote by Xw the set of elements of X not containing w. For strongly irreducible X and patterns w with shape a d-dimensional cube, we obtain upper and lower bounds on htop (X)−htop (Xw) dependent on the size of w. This extends a result of Lind for d=1 . We also apply our methods to an undecidability question in ℤd symbolic dynamics.

Ruled submanifolds with finite type Gauss map

1994 ◽  
Vol 49 (1-2) ◽  
pp. 42-45 ◽  
Author(s):  
Christos Baikoussis
Keyword(s):  
Finite Type ◽  
Gauss Map
Sign in / Sign up

Export Citation Format

Share Document