8 research outputs found
Geometry of differential operators of second order, the algebra of densities, and groupoids
Odd symmetric tensors, and an analogue of the Levi-Civita connection for odd symplectic structure
We consider odd Poisson (odd symplectic) structure on supermanifolds induced
by an odd symmetric rank (non-degenerate) contravariant tensor field. We
describe the difference between odd Riemannian and odd symplectic structure in
terms of the Cartan prolongation of the corresponding Lie algebras, and
formulate an analogue of the Levi-Civita theorem for an odd symplectic
supermanifold
Mercator's projection, logarithm and seafaring
The principal mathematical content of this paper amounts to a classical proposition:
"the cylinder is the uniformising surface for the
logarithm".
We believe that this interpretation of the Mercator projection as the logarithm in the complex domain should be part of every course of complex analysis -- but, unfortunately, we failed to find this simple observation in modern undergraduate textbooks