This work investigates alpha curvature conditions in Kenmotsu manifolds, suggesting strong geometric implications.
The present work aims to investigate Kenmotsu manifolds under prescribed αi-curvature conditions with respect to the connections ∇ and ∇˜. We investigate the geometric consequences of αi- and α˜i-flatness conditions for i=1,2,3,4, and show that these assumptions impose strong restrictions on the underlying geometry, leading to Einstein and η-Einstein structures. Furthermore, curvature derivation conditions of the forms αi(K,L)α4=0 and α˜i(K,L)α˜4=0 for i=1,2,3,4 are examined under both mentioned connections, and the corresponding curvature characterizations are obtained.
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Can et al. (2026) studied this question.
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