Wiener–Tauberian type theorems for radial sections of homogenous vector bundles on certain rank one Riemannian symmetric spaces of noncompact type

2010 ◽  
Vol 269 (1-2) ◽  
pp. 555-586 ◽  
Author(s):  
Sanjoy Pusti ◽  
Swagato K. Ray ◽  
Rudra P. Sarkar
Keyword(s):  
Symmetric Spaces ◽  
Vector Bundles ◽  
Noncompact Type ◽  
Tauberian Type ◽  
Rank One ◽  
Riemannian Symmetric Spaces

HYPERSURFACES IN NONCOMPACT COMPLEX GRASSMANNIANS OF RANK TWO

2012 ◽  
Vol 23 (10) ◽  
pp. 1250103 ◽  
Author(s):  
JÜRGEN BERNDT ◽  
YOUNG JIN SUH
Keyword(s):  
Geometric Structure ◽  
Symmetric Spaces ◽  
Second Fundamental Form ◽  
Kähler Structure ◽  
Noncompact Type ◽  
The Second Fundamental Form ◽  
Special Cases ◽  
Rank One ◽  
Higher Rank ◽  
Riemannian Symmetric Spaces

Consider a Riemannian manifold N equipped with an additional geometric structure, such as a Kähler structure or a quaternionic Kähler structure, and a hypersurface M in N. The geometric structure induces a decomposition of the tangent bundle TM of M into subbundles. A natural problem is to classify all hypersurfaces in N for which the second fundamental form of M preserves these subbundles. This problem is reasonably well understood for Riemannian symmetric spaces of rank one, but not for higher rank symmetric spaces. A general treatment of this problem for higher rank symmetric spaces is out of reach at present, and therefore it is desirable to understand this problem better in a few special cases. Due to some conceptual differences between symmetric spaces of compact type and of noncompact type it appears that one needs to consider these two cases separately. In this paper we investigate this problem for the rank two symmetric space SU 2, m/S(U2Um) of noncompact type.

scholarly journals On Riemannian symmetric spaces of rank one

1970 ◽  
Vol 4 (3) ◽  
pp. 236-263 ◽  
Author(s):  
Isaac Chavel
Keyword(s):  
Symmetric Spaces ◽  
Rank One ◽  
Riemannian Symmetric Spaces

Theorems of Ingham and Chernoff on Riemannian symmetric spaces of noncompact type

2020 ◽  
Vol 279 (11) ◽  
pp. 108760
Author(s):  
Mithun Bhowmik ◽  
Sanjoy Pusti ◽  
Swagato K. Ray
Keyword(s):  
Symmetric Spaces ◽  
Noncompact Type ◽  
Riemannian Symmetric Spaces
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