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.

Anna Kimaczyńska, The grad div operator