17 citations · 30 across the 5 of their papers we have counts for
6 papers
Logarithmic spirals on surfaces of constant Gaussian curvature
Casey Blacker, Pavel Tsyganenko
We compute the geodesic curvature of logarithmic spirals on surfaces of constant Gaussian curvature. In addition, we show that the asymptotic behavior of the geodesic curvature is…
Reduction of -Algebras of Observables on Multisymplectic Manifolds
Casey Blacker, Antonio Michele Miti, Leonid Ryvkin
We develop a reduction scheme for the -algebra of observables on a premultisymplectic manifold in the presence of a compatible Lie algebra action $\mathfrak{g}\cu…
Reduction of multisymplectic manifolds
Casey Blacker
We extend the Marsden-Weinstein-Meyer symplectic reduction theorem to the setting of multisymplectic manifolds. In this context, we investigate the dependence of the reduced space…
Quantization of Polysymplectic Manifolds
Casey Blacker
We adapt the framework of geometric quantization to the polysymplectic setting. Considering prequantization as the extension of symmetries from an underlying polysymplectic manifol…
Polysymplectic Reduction and the Moduli Space of Flat Connections
Casey Blacker
A polysymplectic structure is a vector-valued symplectic form, that is, a closed nondegenerate 2-form with values in a vector space. We first outline the polysymplectic Hamiltonian…
First eigenvalue of the -Laplacian on Kähler manifolds
Casey Blacker, Shoo Seto
We prove a Lichnerowicz type lower bound for the first nontrivial eigenvalue of the -Laplacian on Kähler manifolds. Parallel to the case, the first eigenvalue lower boun…