Acknowledgement
The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A3B05050223) and the second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1I1A3051852).
References
- B.-Y. Chen, Pseudo-Riemannian geometry, δ-invariants and applications, World Sci. Publ., Hackensack, NJ, 2011. https://doi.org/10.1142/9789814329644
- O. Ciaurri, E. Fernandez, and L. Roncal, Revisiting floating bodies, Expo. Math. 34 (2016), no. 4, 396-422. https://doi.org/10.1016/j.exmath.2016.06.001
- J. Jeronimo-Castro and C. Yee-Romero, Characterizations of the Euclidean ball by intersections with planes and slabs, Amer. Math. Monthly 126 (2019), no. 2, 151-157. https://doi.org/10.1080/00029890.2019.1537759
- D.-S. Kim, Ellipsoids and elliptic hyperboloids in the Euclidean space 𝔼n+1, Linear Algebra Appl. 471 (2015), 28-45. https://doi.org/10.1016/j.laa.2014.12.014
- D.-S. Kim and Y. H. Kim, New characterizations of spheres, cylinders and W-curves, Linear Algebra Appl. 432 (2010), no. 11, 3002-3006. https://doi.org/10.1016/j.laa.2010.01.006
- D.-S. Kim and Y. H. Kim, Some characterizations of spheres and elliptic paraboloids, Linear Algebra Appl. 437 (2012), no. 1, 113-120. https://doi.org/10.1016/j.laa.2012.02.013
- D.-S. Kim and Y. H. Kim, Some characterizations of spheres and elliptic paraboloids II, Linear Algebra Appl. 438 (2013), no. 3, 1356-1364. https://doi.org/10.1016/j.laa.2012.08.024
- D.-S. Kim and Y. H. Kim, A characterization of concentric hyperspheres in ℝn, Bull. Korean Math. Soc. 51 (2014), no. 2, 531-538. https://doi.org/10.4134/BKMS.2014.51.2.531
- D.-S. Kim, I. Kim, and Y. H. Kim, Volume properties and some characterizations of ellipsoids in 𝔼n+1, Turkish J. Math. 45 (2021), no. 2, 896-908. https://doi.org/10.3906/mat-2009-36
- D.-S. Kim, Y. H. Kim, and D. W. Yoon, On standard imbeddings of hyperbolic spaces in the Minkowski space, C. R. Math. Acad. Sci. Paris 352 (2014), no. 12, 1033-1038. https://doi.org/10.1016/j.crma.2014.09.003
- D.-S. Kim and B. Song, A characterization of elliptic hyperboloids, Honam Math. J. 35 (2013), no. 1, 37-49. https://doi.org/10.5831/HMJ.2013.35.1.37
- R. Schneider, A characteristic property of the ellipsoid, Amer. Math. Monthly 74 (1967), 416-418. https://doi.org/10.2307/2314577