<Emphasis Type="Italic">N</Emphasis> = 1 Supersymmetric Sigma Model with Boundaries,I

 We study an N=1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N=1 superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures. Received: 27 November 2001 / Accepted: 16 August 2002 Published online: 19 December 2002 Acknowledgements. We are grateful to Ingemar Bengtsson and Andrea Cappelli for discussions and comments. MZ would like to thank the ITP, Stockholm University, where part of this work was carried out. UL acknowledges support in part by EU contract HPNR-CT-2000-0122 and by NFR grant 650-1998368. Communicated by R.H. Dijkgraaf