Linear Independence of Sets of Three Algebraic Curvature Tensors

@inproceedings{Lovell2011LinearIO,
  title={Linear Independence of Sets of Three Algebraic Curvature Tensors},
  author={Britney Kara Lovell},
  year={2011}
}
  • Britney Kara Lovell
  • Published 2011
Looking at the dependence relationship between algebraic curvature tensors gives us an idea of how we can define an algebraic curvature tensor in terms of a linear combination of others. Given that φ is symmetric and ψi skew-symmetric, knowing when {Rφ, Rψ1 , . . . , Rψn} is linearly dependent is just one way of looking at this problem. In this study, we attempt to narrow down the problem by find some cases of when {Rφ, Rψ1 , . . . , Rψn} is linearly independent. We will show {Rφ, Rψ1} and {R… CONTINUE READING