A generalized Wintgen inequality in quaternion Kähler geometry. (English) Zbl 07910083
Summary: In this paper, we establish a generalized Wintgen inequality for quaternionic bi-slant submanifolds and QR-submanifolds (with minimal codimension) in quaternion space forms. We also aim to characterize the second fundamental form of those submanifolds for which the equality cases can hold. Finally, we provide examples of submanifolds embedded in quaternion space forms to support our results.
MSC:
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
Keywords:
normalized scalar curvature; scalar curvature; mean curvature; quaternion space form; DDVV conjecture; bi-slant submanifold; QR-submanifoldReferences:
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