Remarks on an inequality involving the normal scalar curvature

By F. Dillen, Johan Fastenakels, J. Veken. 2006

47 citations recorded by the source corpus.

We study a pointwise inequality for submanifolds in real space forms involving the scalar curvature, the normal scalar curvature and the mean curvature. We translate it into an algebraic problem, allowing us to prove a slightly weaker version of it. We also prove the conjecture for certain types of submanifolds of $\mathbb C^n$.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/1784653b45eaa7123fc01ec43b98df6d46d55b98

How researchers see this paper

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In Applied Mathematics

1. Zhiqin Lu
2. Zizhou Tang
3. Jianquan Ge
4. Zizhou Tang
5. Tom Choi
6. Jianquan Ge
7. Duong H. Phong
8. Jacob Sturm

In Astronomy and Astrophysics

1. Zizhou Tang
2. Jianquan Ge
3. Zizhou Tang
4. Zhiqin Lu
5. Tom Choi
6. Jianquan Ge

Citations in the corpus

• A PROOF OF THE DDVV CONJECTURE AND ITS EQUALITY CASE (2008, methodology): “Since this is a pointwise inequality, one can see using the Gauss and Ricci identities that it’s equivalent to the following algebraic inequality (see [Dillen et al. 2007]):”
• Normal Scalar Curvature Conjecture and its applications (2008, background): “In [8], a weaker version of P (n,m) was proved by using an algebraic inequality in [10] (see also [3]) .”
• On the DDVV conjecture and the comass in calibrated geometry (I) (2006, background): “Let x ∈ M be a fixed point and let (hrij) (i, j = 1, · · · , n and r = 1, · · · ,m) be the coefficients of the second fundamental form under some orthonormal basis.”
• A proof of the DDVV conjecture and its equality case (2008, methodology): “For general n, m, a weaker version was proved in [DFV].”