The proof of concept: a complete solution for the 3-dimensional sphere

Konrad Schöbel ()
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Konrad Schöbel: Friedrich-Schiller-Universität Jena

Chapter 2 in An Algebraic Geometric Approach to Separation of Variables, 2015, pp 55-97 from Springer

Abstract: Abstract Given a scalar product g on V, we can raise and lower indices. The symmetries (0.6a) and (0.6b) then allow us to regard an algebraic curvature tensor $${{R}_{a\text{1}\ a\text{2}\ b\text{1}\ b\text{2}}}$$ on V as a symmetric endomorphism $${{R}^{a\text{1}\ b\text{1}}}_{a\text{2}\ b\text{2}}$$ on the space ʌ2 V of 2-forms on V . Since we will frequently change between both interpretations, we denote endomorphisms by the same letter in boldface.

Date: 2015
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DOI: 10.1007/978-3-658-11408-4_3

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