A Comparative Analysis on the Range of Various Geometrically Moment Maps |
We begin by identifying a moment map in a rather generalsetting, and then see how the ideas work in some more specific situations. Wehope to show that the moment map point of view is useful, both in understandingcertain established results and also in suggesting new problems in geometry andanalysis. While these analytical questions are the main motivation for the work,we will concentrate here on the formal aspects and will not make any seriousinroads on the analysis. More than twenty years back, Atiyah watched that the bendcould be seen as a minute guide for the activity of the measure gathering onthe space of connections. Since then, this thought of a minute guide connectedto boundless dimensional symmetry gatherings underlying various-geometricissues has turned out to be extremely productive. It yields an unifiedperspective on numerous distinctive inquiries, and carries with it a bundle ofstandard hypothesis which can either be connected straight or in any event, inthe deeper perspectives, prescribes what one should attempt to demonstrate. Inthis paper we will first overview briskly a percentage of the overall maderequisitions of these thoughts in the written works.