Include PDF on the same page

This solves the problem :-)

\includepdf[pages=1,pagecommand={\subsection{Kopie des Projektantrages} \thispagestyle{empty}}, fitpaper=true]{\antrag}
\includepdf[pages=2-,pagecommand={\thispagestyle{empty}}, fitpaper=true]{\antrag}

\inlcludepdf always inserts the content on separate pages, because it inserts the pdf-document into your document. If you want the pdf to appear on a page within your document you have to use \includegraphics, which works perfectly fine with pdf files as images in pdflatex.

\usepackage{graphicx}
\subsection{Kopie des Projektantrages}
\includegraphics{antrag.pdf}

Edit: In regard to Dolphins comment: Yes, I think that only works when the pdf file has only one page.