Appendix E. Reilly's Formula
Appendix E reports on an integral formula due to E. Reilly (1973).
Keywords: Newton operator; Reilly's formula.
Let
M and
N be two oriented Riemannian manifolds of dimensions
n and
n − 1 respectively where
M is allowed to have a boundary i.e.,
. Let
be a smooth local orthonormal frame on
M defined on the open set
U ⊂
M. Let
be the corresponding dual coframe i.e.,
. Let ∇ be the Levi-Civita connection of
M and
R its curvature ...
. Let
be a smooth local orthonormal frame on
M defined on the open set
U ⊂
M. Let
be the corresponding dual coframe i.e.,
. Let ∇ be the Levi-Civita connection of
M and
R its curvature ...Get Harmonic Vector Fields now with the O’Reilly learning platform.
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