On extension of isometries on the unit spheres of -spaces for

2011 ◽  
Vol 74 (18) ◽  
pp. 6981-6987 ◽  
Author(s):  
Dong-Ni Tan
Keyword(s):  
Extension Of Isometries

The Integral Extension of Isometries of Quadratic Forms Over Local Fields

1966 ◽  
Vol 18 ◽  
pp. 920-942 ◽  
Author(s):  
Allan Trojan
Keyword(s):  
Vector Space ◽  
Quadratic Forms ◽  
Sufficient Conditions ◽  
Local Fields ◽  
The Other ◽  
Quadratic Space ◽  
Integral Extension ◽  
Ring Of Integers ◽  
Extension Of Isometries ◽  
Necessary And Sufficient

Let F be a local field with ring of integers 0 and prime ideal π0. If V is a vector space over F, a lattice L in F is defined as an 0-module in the vector space V with the property that the elements of L have bounded denominators in the basis for V. If V is, in addition, a quadratic space, the lattice L then has a quadratic structure superimposed on it. Two lattices on V are then said to be isometric if there is an isometry of V that maps one onto the other.In this paper, we consider the following problem: given two elements, v and w, of the lattice L over the regular quadratic space V, find necessary and sufficient conditions for the existence of an isometry on L that maps v onto w.

Extension of Isometries in Finite-Dimensional Indefinite Scalar Product Spaces and Polar Decompositions

1997 ◽  
Vol 18 (3) ◽  
pp. 752-774 ◽  
Author(s):  
Yuri Bolshakov ◽  
Cornelis V. M. van der Mee ◽  
André C. M. Ran ◽  
Boris Reichstein ◽  
Leiba Rodman
Keyword(s):  
Scalar Product ◽  
Product Spaces ◽  
Finite Dimensional ◽  
Extension Of Isometries
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