Riemannian Calculus of Variations Using Strongly Typed Tensor Calculus

In this paper, the notion of strongly typed language will be borrowed from field computer programming to introduce a calculational framework for linear algebra and tensor calculus purpose detecting errors resulting inherent misuse objects finding natural formulations various objects. A bundle formalism, crucially relying on pullback bundle, used create rich type system with which distinguish The relevant notation is designed “telescope” accommodate level detail appropriate set calculations. Various techniques using formalism developed demonstrated goal providing relatively complete uniform method coordinate-free computation. variations pertaining maps between Riemannian manifolds formulated associated techniques. Energy functionals defined in terms first-order Lagrangians are focus second half first variation, Euler–Lagrange equations, variation such derived.