<p>what is the syntax for the sendkey for rightarrow  in .net?</p>

What you are looking for is called spatial search. I'm not sure if there are extensions to  Lucene.Net to do this but you could take a look at
NHibernate Spatial
. Other than that, these queries are often done within the database. At least PostGreSQL, MySQL and SQL Server 2008 have spatial query capabilities.