Classification of the Mappings of (n + 1)- and (n + 2)-Dimensional Spheres into an n-Dimensional Sphere

2022 ◽  
pp. 211-249
Author(s):  
P. S. V. Naidu
Keyword(s):  
Dimensional Sphere

On p-local homotopy types of gauge groups

2014 ◽  
Vol 144 (1) ◽  
pp. 149-160 ◽  
Author(s):  
Daisuke Kishimoto ◽  
Akira Kono ◽  
Mitsunobu Tsutaya
Keyword(s):  
Gauge Group ◽  
Homotopy Type ◽  
Principal Bundle ◽  
Dimensional Sphere ◽  
Gauge Groups ◽  
Homotopy Types

The aim of this paper is to show that the p-local homotopy type of the gauge group of a principal bundle over an even-dimensional sphere is completely determined by the divisibility of the classifying map by p. In particular, for gauge groups of principal SU(n)-bundles over S2d for 2 ≤ d ≤ p − 1 and n ≤ 2p − 1, we give a concrete classification of their p-local homotopy types.

scholarly journals Homotopy Classification of Mappings of a 4-Dimensional Complex into a 2-Dimensional Sphere

1953 ◽  
Vol 5 ◽  
pp. 127-144 ◽  
Author(s):  
Nobuo Shimada
Keyword(s):  
Dimensional Sphere ◽  
Homotopy Classification ◽  
Homotopy Classes ◽  
Cup Product

Steenrod [1] solved the problem of enumerating the homotopy classes of maps of an (n + 1)-complex K into an n-sphere Sn utilizing the cup-i-product, the far-reaching generalization of the Alexander-Čech-Whitney cup product [7] and the Pontrjagin *-product [5].

XX.—Differential Geometry on Hypersurfaces in a Cayley Space

1964 ◽  
Vol 66 (4) ◽  
pp. 216-231 ◽  
Author(s):  
K. Yano ◽  
T. Sumitomo
Keyword(s):  
Complex Structure ◽  
Hermitian Structure ◽  
Dimensional Euclidean Space ◽  
Dimensional Sphere ◽  
Almost Complex Structure ◽  
Principal Curvatures ◽  
Totally Umbilical ◽  
Almost Complex ◽  
Necessary And Sufficient

A seven-dimensional Euclidean space considered as the space of purely imaginary Cayley numbers is called a Cayley space. The six-dimensional sphere in a Cayley space admits an almost complex structure which is not integrable. Moreover the algebraic properties of the imaginary Cayley numbers induce an almost complex structure on any oriented differentiable hypersurface in the Cayley space. The Riemannian metric induced on the hypersurface from the metric of the Cayley space is Hermitian with respect to the almost complex structure.It is proved that the induced Hermitian structure of an oriented hypersurface in the Cayley space is almost Kaehlerian if and only if it is Kaehlerian, that a necessary and sufficient condition for a hypersurface in a Cayley space to be an almost Tachibana space is that the hypersurface be totally umbilical, and that a totally umbilical hypersurface in a Cayley space admits a complex structure when and only when it is totally geodesic.For a hypersurface in the Cayley space with the induced Hermitian structure which is an *O-space it is proved that all the principal curvatures of the hypersurface are constant, and from this is deduced a classification of such *O-spaces.

scholarly journals Classification of tilings of the 2-dimensional sphere by congruent triangles

2002 ◽  
Vol 32 (3) ◽  
pp. 463-540 ◽  
Author(s):  
Yukako Ueno ◽  
Yoshio Agaoka
Keyword(s):  
Dimensional Sphere

THREE-DIMENSIONAL CR-SUBMANIFOLDS IN THE NEARLY KÄHLER 6-SPHERE WITH ONE-DIMENSIONAL NULLITY

2009 ◽  
Vol 20 (02) ◽  
pp. 189-208 ◽  
Author(s):  
MIRJANA DJORIĆ ◽  
LUC VRANCKEN
Keyword(s):  
Three Dimensional ◽  
Dimensional Sphere ◽  
Totally Geodesic ◽  
One Dimensional ◽  
3 Dimensional ◽  
Totally Geodesic Submanifolds ◽  
Nearly Kähler ◽  
Nullity Distribution ◽  
Cr Submanifolds

In this paper, we study certain three-dimensional CR-submanifolds M of the nearly Kähler 6-dimensional sphere S6(1). It is well known that there does not exist a three-dimensional totally geodesic proper CR-submanifold in S6(1). In this paper we obtain a classification of the 3-dimensional CR-submanifolds which are the closest possible to totally geodesic submanifolds, i.e. those that admit a one-dimensional nullity distribution.

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