Off-campus UMass Amherst users: To download dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
Complex supermanifolds
Abstract
In this dissertation we study some properties of a complex supermanifold $M$ = ($X$, ${\cal O}\sb{M}$). In Chapter II we compute the dolbeault cohomology of a superextension of degree 1 over $\IP\sp1$. It is shown that infinitely many of the dolbeault groups are non-zero. In Chapter III we deal with Kahler metrics. We prove that if a metric is Kahler then it osculates to order II. We also compute all the Kahler metrics on some low-dimensional superdomains. Chapter IV gives partial answers to the question: if $\omega$ is a Kahler metric on $X$, when does $\omega$ extend to a superkahler metric on $M$.
Subject Area
Mathematics
Recommended Citation
Julianelle, Anthony, "Complex supermanifolds" (1990). Doctoral Dissertations Available from Proquest. AAI9110159.
https://scholarworks.umass.edu/dissertations/AAI9110159