The Grad Div Operator in Symmetric Tensors on Riemannian Manifolds

The Grad Div Operator in Symmetric Tensors on Riemannian Manifolds

Explore the natural differential operators in the bundle of symmetric tensors on a Riemannian manifold in this 16-minute conference talk from the HyperComplex Seminar 2023. Delve into the investigation of two key operators: the gradient and the divergence, defined analogously to H. M. Rummler's definitions for skew-symmetric forms. Discover the intriguing second-order linear differential operator 'div grad', a result of composing divergence and gradient, and focus on the main subject of research: the 'grad div' operator. Gain insights into symmetric tensors, symmetric derivatives, and their applications in complex and real analysis of several variables.