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Publications [#318262] of Robert Bryant
search www.ams.org.Papers Published
 Bryant, RL, Second order families of special Lagrangian 3folds,
in Perspectives in Riemannian Geometry, CRM Proceedings and Lecture Notes, edited by Vestislav Apostolov, Andrew Dancer, Nigel Hitchin, and McKenzie Wang,
Perspectives in Riemannian Geometry, CRM Proceedings and Lecture
Notes, edited by Vestislav Apostolov, Andrew Dancer, Nigel Hitchin, and
McKenzie Wang, vol. 40 (2006), American Mathematical Society, vol. 40
(2006),
pp. 6398, American Mathematical Society, ISBN 0821838520 [math.DG/0007128]
(last updated on 2017/12/12)
Abstract: A second order family of special Lagrangian submanifolds of complex mspace
is a family characterized by the satisfaction of a set of pointwise conditions
on the second fundamental form. For example, the set of ruled special
Lagrangian submanifolds of complex 3space is characterized by a single
algebraic equation on the second fundamental form.
While the `generic' set of such conditions turns out to be incompatible,
i.e., there are no special Lagrangian submanifolds that satisfy them, there are
many interesting sets of conditions for which the corresponding family is
unexpectedly large. In some cases, these geometrically defined families can be
described explicitly, leading to new examples of special Lagrangian
submanifolds. In other cases, these conditions characterize already known
families in a new way. For example, the examples of LawlorHarvey constructed
for the solution of the angle conjecture and recently generalized by Joyce turn
out to be a natural and easily described second order family.


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