The Collaborative International Dictionary of English v.0.48:

Rigidly \Rig"id*ly\, v.
   In a rigid manner; stiffly.
   [1913 Webster]

WordNet (r) 3.0 (2006):

rigidly
    adv 1: in a rigid manner; "the body was rigidly erect"; "he sat
           bolt upright" [syn: rigidly, stiffly, bolt]

Moby Thesaurus II by Grady Ward, 1.0:

71 Moby Thesaurus words for "rigidly":
   abidingly, absolutely, adamantly, always, changelessly, dead,
   definitely, directly, dourly, enduringly, even, exactly, expressly,
   faithfully, firmly, grimly, hardly, immovably, immutably,
   implacably, impliably, in all respects, in every respect,
   inexorably, inflexibly, intransigently, invariably,
   ipsissimis verbis, ironhandedly, irreconcilably, just, lastingly,
   literally, literatim, obdurately, permanently, perpetually, plumb,
   point-blank, positively, precisely, primly, relentlessly, right,
   rigorously, square, squarely, statically, steadfastly, sternly,
   stiffly, stiltedly, straight, strictly, to the letter, unalterably,
   unbendingly, unchangeably, unchangingly, uncompromisingly,
   undeviatingly, unerringly, unregenerately, unrelentingly,
   unwaveringly, unyieldingly, verbally, verbatim,
   verbatim et litteratim, word by word, word for word