Absos Ali Shaikh, Prosenjit Mandal, Chandan Kumar Mondal
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Splitting theorem of gradient \(\rho \)-Einstein solitons
In this paper, we have proved a weighted Laplacian comparison of distance function for manifolds with Bakry–Émery curvature bounded from below. Next, we have shown that a gradient \(\rho \)-Einstein soliton with a bounded integral condition on Ricci curvature splits off a line isometrically. Moreover, using this result, we have established some boundedness conditions on scalar curvature of gradient \(\rho \)-Einstein soliton.
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