ISOMETRIC IMMERSIONS IN 3-DIMENSIONAL EUCLIDEAN SPACE
نویسندگان
چکیده
In this paper, we examine the image of geodesic curves Riemann 2-manifolds under isometric immersions, in three dimensional Euclidean space. We show that curvature these is equal to normal manifold direction tangent vector field geodesics. Moreover, prove if parameter are line curvature, then torsion geodesics curve.
منابع مشابه
Isometric Immersions into 3-dimensional Homogeneous Manifolds
We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of the metric, the second fundamental form, and data arising from an ambient Killing field. This class of 3-manifolds includes in particular the Berger spheres,...
متن کاملFUZZY HV -SUBSTRUCTURES IN A TWO DIMENSIONAL EUCLIDEAN VECTOR SPACE
In this paper, we study fuzzy substructures in connection withHv-structures. The original idea comes from geometry, especially from thetwo dimensional Euclidean vector space. Using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. We connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as Hv-groups...
متن کاملParallel Transport Frame in 4 -dimensional Euclidean Space
In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...
متن کاملDouble Point Manifolds of Immersions of Spheres in Euclidean Space
Anyone who has been intrigued by the relationship between homotopy theory and diierential topology will have been inspired by the work of Bill Browder. This note contains an example of the power of these interconnections. We prove that, in the metastable range, the double point manifold a self-transverse immersion S n # R n+k is either a boundary or bordant to the real projective space RP n?k. ...
متن کاملCharacterizations of Slant Ruled Surfaces in the Euclidean 3-space
In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Eskis?ehir teknik u?niversitesi bilim ve teknoloji dergisi b- teorik bilimler
سال: 2021
ISSN: ['2667-419X']
DOI: https://doi.org/10.20290/estubtdb.648030