scholarly journals On a Borsuk-Ulam theorem for Stiefel manifolds

1995 ◽  
Vol 71 (2) ◽  
pp. 33-34
Author(s):  
Osamu Yokoyama
Keyword(s):  
Stiefel Manifolds ◽  
Ulam Theorem

scholarly journals Maps of Stiefel manifolds and a Borsuk–Ulam theorem

1989 ◽  
Vol 32 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Jan Jaworowski
Keyword(s):  
Classical Theorem ◽  
Classical Version ◽  
Stiefel Manifolds ◽  
Ulam Theorem ◽  
Expository Article

We are concerned with the following classical version of the Borsuk–Ulam theorem: Let f:Sn→Rk be a map and let Af = {x∈Sn|fx= f(−x)}. Then, if k≦n, Af≠φ. In fact, theorems due to Yang [17] give an estimation of the size of Af in terms of the cohomology index. This classical theorem concerns the antipodal action of the group G=ℤ2 on Sn. It has been generalized and extended in many ways (see a comprehensive expository article by Steinlein [16]). This author ([9, 10)] and Nakaoka [14] proved “continuous” or “parameterized” versions of the theorem. Analogous theorems for actions of the groups G=S1 or S3 have been proved in [11], and [12]; compare also [4, 5, 6].

Invariant Einstein metrics on $\mathrm{SU}(n)$ and complex Stiefel manifolds

2020 ◽  
Vol 72 (2) ◽  
pp. 161-210 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
Yusuke Sakane ◽  
Marina Statha
Keyword(s):  
Einstein Metrics ◽  
Stiefel Manifolds

Discrete Geodesic Flows on Stiefel Manifolds

2020 ◽  
Vol 310 (1) ◽  
pp. 163-174
Author(s):  
Božidar Jovanović ◽  
Yuri N. Fedorov
Keyword(s):  
Geodesic Flows ◽  
Stiefel Manifolds

scholarly journals Whitehead products in the complex Stiefel manifolds

1983 ◽  
Vol 26 (2) ◽  
pp. 241-251 ◽  
Author(s):  
Yasukuni Furukawa
Keyword(s):  
Stiefel Manifold ◽  
Isotropy Group ◽  
Homotopy Groups ◽  
Stiefel Manifolds

The complex Stiefel manifoldWn,k, wheren≦k≦1, is a space whose points arek-frames inCn. By using the formula of McCarty [4], we will make the calculations of the Whitehead products in the groups π*(Wn,k). The case of real and quaternionic will be treated by Nomura and Furukawa [7]. The product [[η],j1l] appears as generator of the isotropy group of the identity map of Stiefel manifolds. In this note we use freely the results of the 2-components of the homotopy groups of real and complex Stiefel manifolds such as Paechter [8], Hoo-Mahowald [1], Nomura [5], Sigrist [9] and Nomura-Furukawa [6].

On Borel–de Siebenthal Representations

2018 ◽  
Vol 2019 (15) ◽  
pp. 4845-4858
Author(s):  
Jing-Song Huang ◽  
Yongzhi Luan ◽  
Binyong Sun
Keyword(s):  
Analytic Continuation ◽  
Lie Groups ◽  
Discrete Series ◽  
Root Systems ◽  
Stiefel Manifolds ◽  
Simple Lie Groups

AbstractHolomorphic representations are lowest weight representations for simple Lie groups of Hermitian type and have been studied extensively. Inspired by the work of Kobayashi on discrete series for indefinite Stiefel manifolds, Gross–Wallach on quaternonic discrete series and their analytic continuation, and Ørsted–Wolf on Borel–de Siebenthal discrete series, we define and study Borel–de Siebenthal representations (also called quasi-holomorphic representations) associated with Borel–de Siebenthal root systems for simple Lie groups of non-Hermitian type.

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