Inquiries into the Idea of Space: Aurel Bejancu, A Biographical Note

Year 2021, Volume: 14 Issue: 1, 1 - 5, 15.04.2021

Bogdan Suceava

https://doi.org/10.36890/iejg.898955

Abstract

John F. Nash Jr.'s Embedding Theorem, published originally in 1956, states that every Riemannian manifold can be isometrically embedded into some Euclidean space. This fundamental result is a very beautiful and extremely important result in differential geometry, and especially in the geometry of submanifolds. One of the researchers with outstanding contributions in the geometry of submanifolds, as well as in other areas of differential geometry, including its connections with physics, with a long creative career spanning from his first research paper in 1971 to his last in 2016, was Aurel Bejancu. In this biographical note we present his life and we remind with great respect his contributions.

Keywords

CR-submanifolds, Aurel Bejancu, submanifolds, differential geometry, Finsler manifolds

References

• 1] Bejancu, A.: CR submanifolds of a Kaehler manifold. I. Proc. Amer. Math. Soc. 69(1), 135–142 (1978).
• [2] Bejancu, A: CR submanifolds of a Kaehler manifold. II. Trans. Amer. Math. Soc. 250, 333-345 (1979).
• [3] Bejancu, A.: Geometry of CR-submanifolds. Mathematics and its Applications (East European Series), 23. D. Reidel Publishing Co., Dordrecht (1986).
• [4] Bejancu, A.: Finsler geometry and applications. Ellis Horwood Series: Mathematics and its Applications. Ellis Horwood, New York (1990).
• [5] Bejancu A.: Kinematic quantities and Raychaudhuri equations in a 5D universe. European Physical Journal C. 75, Article Number: 346 (2015).
• [6] Bejancu, A., Călin, C.: On the (1 + 3) threading of spacetime with respect to an arbitrary timelike vector field. European Physical Journal C. 75, Article number: 159 (2015).
• [7] Bejancu, A., Kon, M., Yano, K.: CR-submanifolds of a complex space form. J. Differential Geometry. 16(1), 137–145 (1981).
• [8] Bejancu, A., Farran, H. R.: Geometry of pseudo-Finsler submanifolds. Kluwer Academic Publishers, Dordrecht (2000).
• [9] Bejancu, A., Farran, H.R.: Foliations and geometric structures. Mathematics and Its Applications, vol. 580. Springer, Dordrecht (2006).
• [10] Chen, B.-Y.: Book Review: Geometry of CR-submanifolds by A. Bejancu, Bull. Amer. Math. Soc. 35, 149–152 (1987).
• [11] Dragomir, S., Shahid, M. H., Al-Solamy, F. R. (editors): Geometry of Cauchy–Riemann Submanifolds. Springer (2016).
• [12] Duggal, K. L., Bejancu, A.: Lightlike submanifolds of semi-Riemannian manifolds and applications. Mathematics and its Applications, 364. Kluwer Academic Publishers Group, Dordrecht (1996).
• [13] Kobayashi, Sh.: MathSciNet Review MR0633633 (83h:53045) to Bejancu, A., Kon, M., Yano, K., CR-submanifolds of a complex space form. J. Differential Geometry 16(1), 137–145 (1981).
• [14] Marques, F. C., Neves, A.: Min-max theory and the Willmore conjecture. Annals of Mathematics. 179, 683–782 (2013).
• [15] Ogiue, K.: MathSciNet Review MR0467630 (57 #7486) of Bejancu, A.: CR submanifolds of a Kaehler manifold. I. Proc. Amer. Math. Soc. 69(1), 135–142 (1978).
• [16] Shen, Z.: MathSciNet Review MR1861512 (2003d:53125) of Bejancu, A., Farran, H. R., Geometry of pseudo-Finsler submanifolds, Kluwer Academic Publishers, Dordrecht (2000).
• [17] Singh, S. S.: MathSciNet Review MR1071171 (91i:53075) to Bejancu, A.: Finsler geometry and applications. Ellis Horwood Series: Mathematics and its Applications. Ellis Horwood, New York (1990).
• [18] Suceavă, B. D.: The Cartan connection: sketches for a portrait of Kentaro Yano. Creat. Math. Inform. 29(2), 237–242 (2020).
• [19] Willmore, T. J.: Note on embedded surfaces. An. Şti. Univ. “Al. I. Cuza” Iaşi, Secţ I a Mat. (N.S.) 11B, 493–496 (1965).