caa a22 4500 606200967 CHVBK 20210128100946.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00025-014-0421-3 doi (NATIONALLICENCE)springer-10.1007/s00025-014-0421-3 Suceavă Bogdan Department of Mathematics, California State University at Fullerton, 92834-6850, Fullerton, CA, USA aut On Strongly Minimal Kähler Surfaces in $${\mathbf{C}^3}$$ C 3 and the Equality $${scal(p) [Elektronische Daten] 4 \inf sec(\pi ^r)}$$ s c a l ( p ) = 4 inf s e c ( π r ) [Bogdan Suceavă] Pursuing an idea motivated by a question of S.-S. Chern from 1968 on the existence of intrinsic Riemannian obstructions to minimality [Chern, S.-S.: Minimal submanifolds in a Riemannian manifold (1968)], an important study of the very idea of curvature was deepened after 1993 by B.-Y. Chen, then by other authors. In the last two decades, B.-Y. Chen's fundamental inequalities have been investigated by many authors in the context of various geometric structures. In this work, we start by presenting B.-Y. Chen's fundamental inequality for Kähler submanifolds in complex space forms, and we recall why the case of Kähler surfaces in $${\mathbf{C}^3}$$ C 3 satisfying $${scal(p) = 4 \inf sec(\pi ^r)}$$ s c a l ( p ) = 4 inf s e c ( π r ) appears naturally and is important. Then we provide several characterizations of strongly minimal complex surfaces in the complex three dimensional space. We focus our study on the question of finding further examples of strongly minimal Kähler surfaces, as the question of a complete classification of these geometric objects is still open. Springer Basel, 2014 Minimal submanifods nationallicence Kähler submanifolds nationallicence strongly minimal submanifolds nationallicence Chen invariants nationallicence Results in Mathematics Springer Basel 68/1-2(2015-09-01), 45-69 1422-6383 68:1-2<45 2015 68 25 https://doi.org/10.1007/s00025-014-0421-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-014-0421-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Suceavă Bogdan Department of Mathematics, California State University at Fullerton, 92834-6850, Fullerton, CA, USA aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 68/1-2(2015-09-01), 45-69 1422-6383 68:1-2<45 2015 68 25