Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 1, pp. 285300 (2008) 

Variations of (para)Hodge structures and their period maps in tt*geometryLars SchäferD20146 Hamburg, Germany, email: schaefer@math.unihamburg.deAbstract: We introduce the notion of variations of Hodge structures (VHS) in paracomplex geometry and define the associated period map. Moreover, we construct VHS from special (pa\ra)complex and (para)Kähler manifolds and prove that they provide solutions of (metric) $tt^*$bundles (cf. [H] for the complex case). In the case of odd weight we relate the period map to the (para)pluriharmonic maps associated to $tt^*$bundles (cf. [S2], [S3]). \item[H] C. Hertling: tt*geometry, Frobenius manifolds, their connections, and the construction for singularities. J. Reine Angew. Math. {\bf 555} (2003), 77161. \item[S2] L. Schäfer, tt*bundles and pluriharmonic maps. Ann. Global Anal. Geom. {\bf 28}(3) (2005), 285300. \item[S3] L. Schäfer, $tt^*$bundles in paracomplex geometry, special paraKähler manifolds and parapluriharmonic maps. Diff. Geom. and Appl. {\bf 24}(1) (2006), 6089. Keywords: tt*bundles, (para)pluriharmonic maps, special (para)complex and special (para)Kähler manifolds, variations of (para)Hodge structure, period maps Classification (MSC2000): 53C43, 58E20, 32G20 Full text of the article:
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