#deRham's thesis, Hodge realized that real and imaginary parts of a #holomorphic 1-form on a #Riemann surface were in some sense dual to each other. He suspected that there should be a similar duality in higher dimensions; this duality is now #Hodge star operator

#deRham's thesis, Hodge realized that real and imaginary parts of a #holomorphic 1-form on a #Riemann surface were in some sense dual to each other. He suspected that there should be a similar duality in higher dimensions; this duality is now #Hodge star operator

operator can be extended to operate on tensors as divergence of the covariant derivative. Alternatively, the operator can be generalized to operate on differential forms using the divergence and exterior derivative. The resulting operator is called Laplace– #deRham operator

operator can be extended to operate on tensors as divergence of the covariant derivative. Alternatively, the operator can be generalized to operate on differential forms using the divergence and exterior derivative. The resulting operator is called Laplace– #deRham operator