On some conjectures by Lu and Wenzel

Abstract

In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this paper we discuss further these conjectures and put forward several new conjectures which will be shown equivalent to Conjecture 2. In particular, we prove Conjecture 2 and hence all conjectures in some special cases. For Conjecture 3, we obtain a bigger upper bound $2+\sqrt{10}/2$, and we also give a weaker answer for the more general Question 1. In addition, we obtain some new simple proofs of the complex BW inequality and the condition for equality.

arXiv comment31 pages

References in corpus (5)

• Normal scalar curvature conjecture and its applications
• Generalizations of Heisenberg uncertainty relation
• DDVV-type inequality for skew-symmetric matrices and Simons-type inequality for Riemannian submersions
• Remarks on an inequality involving the normal scalar curvature
• Recent developments of the DDVV Conjecture

Cited by in corpus (1)

• Some generalizations of the DDVV and BW inequalities