Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 7 1 2026 01 01 Finiteness of fundamental groups in extended complete Einstein-type manifolds 69 75 5921 10.22060/ajmc.2025.23648.1278 EN Ayoub Mohammadalipour Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran Behroz Bidabad Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran 0000-0003-3993-4268 Mohamad Yar Ahmadi Department of Mathematics, Faculty of the Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran Journal Article 2024 11 02 Here, an extension of the complete non-compact Einstein-type manifolds is studied and shows that it has a finite fundamental group. This paper generalizes Wylie's results to the setting of extended Einstein-type manifolds for certain parameters. Some direct corollaries of this result are also pointed out. For instance, the sphere bundle $SM$ has a finite fundamental group. These findings not only generalize previous results but also offer new insights into the applications of Einstein-type manifolds across mathematics and physics, particularly in the structure of associated bundles and the behavior of geometric flows. https://ajmc.aut.ac.ir/article_5921_b59442085644532ef03417a3e5a76437.pdf