Is there a way to create an Android Web Application like on the iPhone?
Using the "apple-mobile-web-app-capable" meta tag in the head element of an HTML page, it informs the Apple iOS that the application can be installed to the users springboard so that it starts the Safari Mobile browser without a menu bar.
Chrome on Android now supports a meta-tag mobile-web-app-capable:
Since Chrome M31, you can set up your web app to have an application shortcut icon added to a device's homescreen, and have the app launch in full-screen "app mode" using Chrome for Android’s "Add to homescreen" menu item.
For details about the mobile-web-app-capable meta-tag, scroll down to "Supporting homescreen-installed apps prior to M39":
Since M31, Chrome will look for the following meta tag in the element of the web-page (if there's a manifest with display specified, this is ignored):
<meta name="mobile-web-app-capable" content="yes">The name attribute MUST be "mobile-web-app-capable" and the content attribute must be "yes" (case in-sensitive). If there is any other value in the content attribute the web app will be added as a regular bookmark.
While I don't have any devices running Chrome M31 that I could test with, I interpret this to mean that full-screen web apps, with an icon on the device's homescreen, are supported as far back as Chrome M31, provided you use that mobile-web-app-capable meta tag.