Developing GIS Application on Android

There was a QGIS Android project as part of this year's Google Summer of Code. Marco Bernasocchi was the author, and although it is largely a work in progress, he has managed to get the basics working on an Android tablet. Just search QGIS Android and you'll come up with several links to mailing list posts, his blog, and download links.

For a proper useable GIS with groprocessing, this is your best (rather, only) option, but it is in the very early stages so you will have to wait until Marco gets more time/funding, or someone carries on development.

I have recently been pursuing research in the same area as you, and have found that there are not currently any open source mobile GIS APIs around that would be suitable to building a client application specifically supported for Android. I did come across BeeGIS but have not had an opportunity to spend any time with it.

Additionally you can refer to this question.

You can try NASA WorldWind. They just started android support with the help of QinetiQ‘s QGlobe team.