{"paper":{"title":"Contact stationary Legendrian surfaces in $S^5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SG"],"primary_cat":"math.DG","authors_text":"Yong Luo","submitted_at":"2012-11-18T15:57:50Z","abstract_excerpt":"Let $(M^5,\\alpha,g_\\alpha,J)$ be a 5-dimensional Sasakian Einstein manifold with contact 1-form $\\alpha$, associated metric $g_\\alpha$ and almost complex structure $J$ and $L$ a contact stationary Legendrian surface in $M^5$. We will prove that $L$ satisfies the following equation\n  \\begin{eqnarray}\\label{equ}\n  -\\Delta^\\nu H+(K-1)H=0, \\end{eqnarray} where $\\Delta^\\nu$ is the normal Laplacian w.r.t the metric $g$ on $L$ induced from $g_\\alpha$ and $K$ is the Gauss curvature of $(L,g)$.\n  Using equation \\eqref{equ} and a new Simons' type inequality for Legendrian surfaces in the standard unit s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4227","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}