Even and odd symplectic and K\"ahlerian structures on projective superspaces

TL;DR

This paper explores the supergeneralization of complex projective spaces through even and odd K"ahlerian structures, analyzing their Hamiltonian reduction, operator properties, and applications in quantization and mechanics.

Contribution

It introduces new supergeometric structures on projective superspaces and examines their roles in Hamiltonian reduction and Batalin--Vilkovisky formalism.

Findings

Construction of even and odd K"ahlerian structures on superspaces

Analysis of operator Δ in quantization formalism

Identification of bi-Hamiltonian properties in mechanics

Abstract

Supergeneralization of $\DC P(N)$ provided by even and odd K\"ahlerian structures from Hamiltonian reduction are construct.Operator $ \Delta$ which used in Batalin-- Vilkovisky quantization formalism and mechanics which are bi-Hamiltonian under corresponding even and odd Poisson brackets are considered.